
ACTA SCIENTIARUM MATHEMATICARUM (Szeged)
Abstract. For a bounded lattice $L$, the principal congruences of $L$ form a bounded ordered set $\princ L$. G. Grätzer proved in 2013 that every bounded ordered set can be represented in this way. Also, G.Birkhoff proved in 1946 that every group is isomorphic to the group of automorphisms of an appropriate lattice. Here, for an arbitrary bounded ordered set $P$ with at least two elements and an arbitrary group $G$, we construct a selfdual lattice $L$ of length sixteen such that $\princ L$ is isomorphic to $P$ and the automorphism group of $L$ is isomorphic to $G$.
DOI: 10.14232/actasm0158178
AMS Subject Classification
(1991): 06B10
Keyword(s):
principal congruence,
lattice congruence,
lattice automorphism,
ordered set,
bounded poset,
quasicolored lattice,
preordering,
quasiordering,
monotone map,
simultaneous representation,
independence,
automorphism group
Received September 6, 2015, and in revised form September 28, 2015. (Registered under 67/2015.)
Tamás Dékány,
Gergő Gyenizse,
Júlia Kulin

1928

Abstract. Slim rectangular lattices were introduced by G. Grätzer and E. Knapp in Acta Sci. Math. 75, 2948, 2009. They are finite semimodular lattices $L$ such that the poset $\jir L$ of joinirreducible elements of $L$ is the cardinal sum of two nontrivial chains. Using deep tools and involved considerations, a 2013 paper by G. Czédli and the present authors proved that a slim semimodular lattice is rectangular iff so is the JordanHölder permutation associated with it. Here, we give an easier and more elementary proof.
DOI: 10.14232/actasm015271y
AMS Subject Classification
(1991): 06C10
Keyword(s):
rectangular lattice,
semimodularity,
slim lattice,
planar lattice,
combinatorics of permutations
Received June 26, 2014, and in revised form March 2, 2015. (Registered under 21/2015.)
Neha Makhijani,
R. K. Sharma,
J. B. Srivastava

2943

Abstract. Let $\mathbb{F}_{p^{k}}A_{5}$ be the group algebra of $A_{5}$, the alternating group of degree $5$, over $\mathbb{F}_{p^{k}}=GF(p^{k})$, where $p$ is a prime. Using the theory developed by Ferraz in [Ferraz08], we give an explicit description for the Wedderburn decomposition of $\mathbb{F}_{p^{k}}A_{5}$ modulo its Jacobson radical.
DOI: 10.14232/actasm0143112
AMS Subject Classification
(1991): 16S34; 16U60
Keyword(s):
group algebra,
Wedderburn decomposition,
unit group
Received August 19, 2014. (Registered under 61/2014.)
Swati Sidana,
R. K. Sharma

4553

Abstract. Let $L=M(G,2)$ be a $RA2$ loop and $F[L]$ be its loop algebra over a field $F$. In this article, we obtain the unit loop of $F[L]/J(F[L]),$ where $L=M(D_{2p},2)$ is obtained from the dihedral group of order $2p$ ($p$ odd prime), $J(F[L])$ is the Jacobson radical of $F[L]$ and $F$ is a finite field of characteristic $2$. The structure of $1+J(F[L])$ is also determined.
DOI: 10.14232/actasm0155066
AMS Subject Classification
(1991): 20N05, 17D05
Keyword(s):
loop algebra,
Moufang loop,
Zorn's algebra,
general linear loop,
loops $M(G,
2)$
Received February 4, 2014, and in revised form August 27, 2015. (Registered under 6/2015.)
K. Tinpun,
J. Koppitz

5563

Abstract. In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.
DOI: 10.14232/actasm0155024
AMS Subject Classification
(1991): 20M20, 54H15
Keyword(s):
generating sets,
transformation semigroups,
restricted range,
relative ranks
Received January 7, 2015, and in revised form September 15, 2015. (Registered under 2/2015.)
Liangying Jiang,
Caiheng Ouyang,
Ruhan Zhao

65100

Abstract. We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>1$). Furthermore, we give some composition operators induced by linear fractional selfmaps of the unit ball $B_N$ that are not essentially normal.
DOI: 10.14232/actasm014060x
AMS Subject Classification
(1991): 47B33; 32A35, 32A36
Keyword(s):
composition operator,
essentially normal,
automorphism,
linear fractional maps
Received August 19, 2014, and in revised form October 19, 2014. (Registered under 60/2014.)
Eszter Gselmann,
Zsolt Páles

101110

Abstract. The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \Eq{*}{ d_{k}(xy)=\sum_{i=0}^{k}\Gamma(i,ki) d_{i}(x)d_{ki}(y) \qquad(x,y\in{\msbm R}, k\in\{0,\ldots,n\}) } is studied, where $\Delta_n:=\big\{(i,j)\in\Z \times\Z \mid0\leq i,j\mbox{ and }i+j\leq n\big\}$ and $\Gamma\colon \Delta_n\to{\msbm R} $ is a symmetric function such that $\Gamma(i,j)=1$ whenever $i\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\dots,d_{n}\colon{\msbm R} \to{\msbm R} $ of the above system of equations is characterized. As a consequence of the main result, for any nonzero real derivation $d\colon{\msbm R} \to{\msbm R} $, the iterates $d^0,d^1,\dots,d^n$ of $d$ are shown to be linearly independent, and the graph of the mapping $x\mapsto(x,d^1(x),\dots,d^n(x))$ to be dense in ${\msbm R} ^{n+1}$.
DOI: 10.14232/actasm0145346
AMS Subject Classification
(1991): 16W25, 39B50
Keyword(s):
derivation,
higher order derivation,
iterates,
linear dependence
Received April 23, 2014, and in revised form August 19, 2014. (Registered under 34/2014.)
S. S. Volosivets,
A. A. Tyuleneva

111124

Abstract. It is well known that for a nonnegative sequence $\{a_n\}_{n=1}^\infty $ the continuity of the sum $\sum ^\infty_{n=1}a_n\cos nx$ is equivalent to the convergence of the series $\sum ^\infty_{n=1}a_n$. We prove that for generalized monotone $\{a_n\}_{n=1}^\infty $ the last condition implies the socalled $p$absolute continuity in the sense of L. C. Young and E. R. Love, where $1< p< \infty $. In this case we give estimates for the $p$variation moduli of continuity and best approximations in terms of Fourier coefficients of a function. As a corollary of the above results some Konyushkovtype theorems on the equivalence of $O$ and $\asymp $relations are established.
DOI: 10.14232/actasm0145744
AMS Subject Classification
(1991): 42A32, 42A10, 42A16, 41A25
Keyword(s):
$p$variation,
$L^p$,
best approximation,
fractional moduli of continuity,
Fourier coefficients,
equivalence of $O$ and $\asymp $relations
Received November 12, 2014, and in revised form August 15, 2015. (Registered under 74/2014.)
Kristóf Szarvas,
Ferenc Weisz

125146

Abstract. The inverse wavelet transform is studied with the help of the summability means of Fourier transforms. Norm and almost everywhere convergence of the inversion formula is obtained for $L_p$ functions. The points of the set of the almost everywhere convergence are characterized as the Lebesgue points.
DOI: 10.14232/actasm0142958
AMS Subject Classification
(1991): 42C40; 42C15, 42B08, 42A38, 46B15
Keyword(s):
continuous wavelet transform,
$\theta $summability,
inversion formula
Received June 10, 2014, and in revised form January 6, 2015. (Registered under 45/2014.)
Abstract. We shall show in this paper a quite useful formula connecting the essential minimum modulus and minimum modulus of any linear bounded operator defined on a separable Hilbert space. Since this formula does not depend on the structure of Hilbert space, this result enables us to define the essential minimum modulus of linear operators in the more general context of Banach spaces. The connection between our definition and that given by Zemánek [Geometric interpretation of the essential minimum modulus, Operator Theory: Adv. Appl., 6, (1982), 225227] is discussed. Moreover, the notion of the essential surjectivity modulus and left (resp. right) essential minimum modulus on Banach spaces are also defined and will be studied in this paper. The asymptotic formula for the essential spectrum of a semiFredholm operator with index zero in terms of the left and right essential minimum moduli is proved.
DOI: 10.14232/actasm0145388
AMS Subject Classification
(1991): 47A53, 47A55, 47A60, 46B04
Keyword(s):
Banach space,
minimum modulus,
surjectivity modulus,
essential minimum modulus,
Calkin algebra,
essential spectrum,
semiFredholm,
index
Received May 14, 2014, and in final form January 17, 2016. (Registered under 38/2014.)
Abdelmonaim El Kaddouri,
Kamal El Fahri,
Mohammed Moussa

165173

Abstract. We introduce a new class of operators that we call blimited operators. Properties of blimited operators, the relationship between the blimited operators and various classes of operators are studied.
DOI: 10.14232/actasm0145702
AMS Subject Classification
(1991): 46B42, 47B60, 47B65
Keyword(s):
order limited operator,
bAMcompact operator,
limited operator,
(b)property,
discrete Banach lattice
Received October 13, 2014, and in final form January 10, 2015. (Registered under 70/2014.)
Zoltán Sebestyén,
Zsigmond Tarcsay

175191

Abstract. We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint and essentially selfadjoint operators due to Nelson, Kato, Rellich, and Wüst. Our method involves the range of twobytwo matrices of the form $M_{S,T}=\soperator{T}{S}$ that makes it possible to treat real and complex Hilbert spaces jointly.
DOI: 10.14232/actasm0158093
AMS Subject Classification
(1991): 47A05, 47A55, 47B25
Keyword(s):
closed operator,
adjoint,
selfadjoint operator,
operator product,
operator sum,
perturbation
Received June 10, 2014, and in revised form January 6, 2015. (Registered under 59/2015.)
Sara BotelhoAndrade

193204

Abstract. In this paper we solve the isometric equivalence problem for composition operators on Hardy spaces of the bidisk, for generalized composition operators on the Bloch space and for elementary operators on the symmetric subspace of $\mathcal{B}(\mathcal{H})$.
DOI: 10.14232/actasm0140440
AMS Subject Classification
(1991): 47A06, 47B25, 47B33
Keyword(s):
isometric equivalence,
Hardy space,
Bloch space,
spaces of symmetric operators,
composition operators,
elementary operators
Received May 31, 2014, and in revised form October 20, 2014. (Registered under 44/2014.)
Pietro Aiena,
Salvatore Triolo

205219

Abstract. Some classical perturbation results on Fredholm theory are proved and extended by using the stability of the localized singlevalued extension property under Riesz commuting perturbations. In the last part, we give some results concerning the stability of property $(gR)$ and property $(gb)$.
DOI: 10.14232/actasm0147851
AMS Subject Classification
(1991): 47A10, 47A11; 47A53, 47A55
Keyword(s):
localized SVEP,
operators with topological uniform descent,
Riesz operators,
property $(gR)$ and property $(gb)$
Received April 17, 2014, and in revised form December 5, 2014. (Registered under 35/2014.)
Carl C. Cowen,
Eungil Ko,
Derek Thompson,
Feng Tian

221234

Abstract. We completely characterize the spectrum of a weighted composition operator \W on \HtD when \ph has DenjoyWolff point $a$ with $0<\ph '(a)< 1$, the iterates, $\ph_n$, converge uniformly to $a$, and $\psi $ is in \Hi(the space of bounded analytic functions on \D ) and continuous at $a$. We also give bounds and some computations when $a=1$ and $\ph '(a)=1$ and, in addition, show that these symbols include all linear fractional \ph that are hyperbolic and parabolic nonautomorphisms. Finally, we use these results to eliminate possible weights $\psi $ so that \W is seminormal.
DOI: 10.14232/actasm014542y
AMS Subject Classification
(1991): 47B33, 47B35, 47A10, 47B20, 47B38
Keyword(s):
weighted composition operator,
spectrum of an operator,
hyponormal operator
Received May 21, 2014, and in revised form September 18, 2014. (Registered under 42/2014.)
H. Bercovici,
W. S. Li

235269

Abstract. We provide a direct, intersection theoretic, argument that the Jordan models of an operator of class $C_{0}$, of its restriction to an invariant subspace, and of its compression to the orthogonal complement, satisfy a multiplicative form of the Horn inequalities, where `inequality' is replaced by `divisibility'. When one of these inequalities is saturated, we show that there exists a splitting of the operator into quasidirect summands which induces similar splittings for the restriction of the operator to the given invariant subspace and its compression to the orthogonal complement. The result is true even for operators acting on nonseparable Hilbert spaces. For such operators the usual Horn inequalities are supplemented so as to apply to all the Jordan blocks in the model.
DOI: 10.14232/actasm015538z
AMS Subject Classification
(1991): 47A15
Keyword(s):
invariant subspaces,
Horn inequalities
Received May 19, 2015. (Registered under 38/2015.)
Abstract. The paper deals with Schattenvon Neumann operators in a Hilbert space. A sharp perturbation bound for invariant subspaces is established. It can be considered as a particular generalization of the DavisKahan theorem.
DOI: 10.14232/actasm015514y
AMS Subject Classification
(1991): 47A15, 47A55, 47B10
Keyword(s):
Hilbert space,
compact operators,
invariant subspaces,
perturbations
Received February 22, 2015, and in revised form April 27, 2015. (Registered under 14/2015.)
B. Chevreau,
A. Crăciunescu

281287

Abstract. A result of Eckstein asserts that for any $\rho $contraction $T$ on a Hilbert space $\mathcal{H}$ the sequence $(T^{n}h)_{n}$ is convergent for any $h\in\mathcal {H}$. We show that this remains true for a natural generalization of the class of $\rho $contractions, which we call the class of $(\rho,N)$contractions (notation: $\mathcal{C}_{\rho,N}(\mathcal{H})$). Our argument follows the lines of Mlak's proof of Eckstein's result, but is somewhat simplified by a study of coisometric $(\rho,N)$dilations of these operators, which seems to be of independent interest. Along the way we also point out that Gavruta's example extends to the class of $(\rho,N)$contractions. Namely, let $\mathcal{C}_{\infty,\infty }(\mathcal{H}) :=\cup_{\rho,N}\mathcal{C}_{\rho,N}(\mathcal{H})$; then, for any integer $p>1$, there exists an operator $T$ such that $T^{p}=I$ and $T\notin\mathcal {C}_{\infty,\infty }(\mathcal{H})$.
DOI: 10.14232/actasm0140042
AMS Subject Classification
(1991): 47A20
Keyword(s):
contractions,
coisometric dilations,
similarity
Received July 18, 2014, and in final form January 5, 2015. (Registered under 4/2014.)
S. Rajesh,
P. Veeramani

289304

Abstract. Brodskii and Milman proved that there exists a point in $C(A)$, the set of all Chebyshev centers of $A$, which is fixed by every surjective isometry from $A$ into $A$ whenever $A$ is a nonempty weakly compact convex set having normal structure in a Banach space. Motivated by this result, Lim et al. proved that every isometry from $A$ into $A$ has a fixed point in $C(A)$ whenever $A$ is a nonempty weakly compact convex set having normal structure in a Banach space. In this paper, we prove that every relatively isometry map $T\colon A\cup B \rightarrow A\cup B$, satisfying $T(A) \subseteq B$ and $T(B) \subseteq A$, has a best proximity point in $C_{A}(B)$, the set of all Chebyshev centers of $B$ relative to $A$, whenever the nonempty weakly compact convex proximal pair $(A, B)$ has proximal normal structure and rectangle property. Also, we prove that, under suitable assumptions, an analogous result of Brodskii and Milman for relatively isometry mappings holds. In case of $A = B$, we obtain the results of Brodskii and Milman, and Lim et al. as a particular case of our results.
DOI: 10.14232/actasm0148331
AMS Subject Classification
(1991): 47H09, 47H10
Keyword(s):
asymptotic center,
Chebyshev center,
best proximity points,
proximal pairs,
relatively nonexpansive maps,
rectangle property
Received December 30, 2014. (Registered under 83/2014.)
Gábor V. Nagy,
Attila Szalai

305312

Abstract. We examine the convexity of the hitting distribution of the real axis for symmetric random walks on $\duz ^2$. We prove that for a random walk starting at $(0,h)$, the hitting distribution is convex on $[h2,\infty )\cap\duz $ if $h\ge2$. We also show an analogous fact for higherdimensional discrete random walks. This paper extends the results of a recent paper [NT].
DOI: 10.14232/actasm0145261
AMS Subject Classification
(1991): 60G50; 05A20
Keyword(s):
discrete random walk,
integer lattice,
convexity
Received April 2, 2014. (Registered under 26/2014.)
Mátyás Barczy,
Gyula Pap,
Tamás T. Szabó

313338

Abstract. We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
DOI: 10.14232/actasm0150160
AMS Subject Classification
(1991): 91G70, 60H10, 62F12, 60F05
Keyword(s):
Heston model,
conditional least squares estimation
Received February 23, 2015, and in revised form October 24, 2015. (Registered under 16/2015.)

339351
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