
ACTA SCIENTIARUM MATHEMATICARUM (Szeged)
Abstract. As an extension of a result in [1] about the semisimple case, left orders in the sense of Fountain and Gould in rings with local units, minimum condition for principal left ideals, and arbitrary radical are characterized by means of covering every finite subset of them by left orders in the classical sense in rings with identity and with minimum condition for principal left ideals.
AMS Subject Classification
(1991): 16P70, 16N40, 16U99
Received October 13, 1993. (Registered under 5566/2009.)
Abstract. A refinement of Á. Szendrei's characterization theorem for simple surjective algebras is given. Moreover, it is shown that every at least three element finite simple nonunary algebra with transitive automorphism group is either functionally complete or affine.
AMS Subject Classification
(1991): 08A40
Received January 7, 1994. (Registered under 5567/2009.)
Abstract. It is shown that every finite, simple, strongly Abelian algebra generating a minimal variety is term equivalent to a full matrix power of a $2$element unary algebra. The proof is based on a classification of reducts of matrix powers of unary algebras.
AMS Subject Classification
(1991): 08B05, 08A40, 08A05
Received January 10, 1994 and in revised form March 14, 1994. (Registered under 5568/2009.)
R. Bělohlávek,
I. Chajda

4347

Abstract. A groupoid $(G;\cdot )$ is left uniquely divisible if for each $a,b\in G$ there exists exactly one $x\in G$ with $a\cdot x=b$. A semiloop is a left uniquely divisible groupoid with a right unit. We characterize ideals of semiloops which are kernels of congruences and we prove that the variety of all semiloops has ideal determined congruences.
AMS Subject Classification
(1991): 08A30, 08B05, 20N05
Keyword(s):
uniquely divisible groupoid,
semiloop,
ideal,
kernel of congruence,
ideal determined congruences
Received June 25, 1991 and in revised form November 29, 1993. (Registered under 5569/2009.)
Abstract. The present paper deals with some conditions characterizing consistence in lower continuous strongly dually atomic lattices.
AMS Subject Classification
(1991): 06B35, 06C05
Received May 11, 1992 and in revised form January 14, 1994. (Registered under 5570/2009.)
JeanClaude Carrega

5359

Abstract. A finite distributive sublattice $T$ of a lattice $L$ is said to have the property $P$ if $T$ is contained in a Boolean sublattice of $L$. We consider the class $\Gamma $ of all lattices $L$ each of whose finite distributive sublattices has the property $P$. We prove that every relatively complemented modular lattice $L$ is in $\Gamma $. If, in addition, $L$ is atomic then we characterize subdirect irreducibility of $L$. A weaker result is given for semimodular lattices.
AMS Subject Classification
(1991): 06D05, 06C05, 06C10
Received September 25, 1992 and in revised form December 13, 1993. (Registered under 5571/2009.)
D. D. Anderson,
C. Jayaram,
P. A. Phiri

6174

Abstract. Let $L$ be a reduced, compactly generated multiplicative lattice in which 1 is compact and every finite product of compact elements is compact. In this setting we study quasiregular lattices (for every compact element $x\in L$, there exists a compact element $y\in L$ with $(0:(0:x))=(0:y))$, regular lattices (every compact element is complemented), and Baer lattices (for every compact element $x$, $(0:x)\vee(0:(0:x))=1)$.
AMS Subject Classification
(1991): 06F10, 06E99
Keyword(s):
quasiregular lattices,
Baer lattices,
multiplicative lattices,
compact elements
Received October 26, 1992 (Registered under 5572/2009.)
Abstract. For an inverse semigroup $S$, we prove that the translational hull of the closure of the idempotents $\Omega(E_S\omega )$ is isomorphic to the closure of the idempotents $E_{\Omega(S)}\omega $ in the translational hull $\Omega(S)$. This characterization gives a new proof for the fact that the translational hull of an $E\omega $Clifford semigroup is $E\omega $Clifford, which was first proved by Reilly [3].
AMS Subject Classification
(1991): 20M15, 20M18, 20M12
Received October 1, 1993. (Registered under 5573/2009.)
Fadhel A. AlMusallam

7992

Abstract. The norm closure of the intermediate orbit of an essentially normal operator acting on an infinite dimensional separable Hilbert space need not contain any normal operator. Two instances of essentially normal operators where the norm closure of the intermediate orbit contains a normal operator are discussed.
AMS Subject Classification
(1991): 47A58
Received August 24, 1992 and in revised form October 20, 1993. (Registered under 5574/2009.)
Lawrence A. Fialkow

93120

Abstract. Given Hilbert space operators $A$ and $B$, we characterize solvability of the operator equation $A = BJ + G$, where $J$ is a Fredholm operator of prescribed index and $G$ is an operator of prescribed finite rank. In the case when $A$ or $B$ has closed range, we characterize solvability of $A = BJ + K$, with $J$ Fredholm and $K$ compact. More generally, for elements $a$, $b$ of a $C^*$algebra ${\cal A}$, we study solvability of the equation $a = bj$, $j$ invertible. There are natural majorization and annihilator conditions necessary for solvability, and we show that if ${\cal A}$ is Rickart, then these conditions are also sufficient.
AMS Subject Classification
(1991): 47A68, 47A62
Received February 10, 1993. (Registered under 5575/2009.)
Abstract. In this paper the relation between the elements of a von Neumann algebra for which a suitable $L^2$ type norm is preserved by an $\omega $conditional expectation to a von Neumann subalgebra and the relevant canonical state extension is discussed. The main tool used is a polar decomposition for operators depending on both the von Neumann algebra and a faithful normal state on it.
AMS Subject Classification
(1991): 46L50
Received June 7, 1993 and in revised form December 28, 1993. (Registered under 5576/2009.)
Abstract. The author showed in [10] that a certain selfdual subnormal operator is represented as the sum of mutually commutative normal operator and a quasinormal operator and also showed that the converse of this theorem is not true, i.e., a pure operator $S$ which is the sum of mutually commutative normal operator and a quasinormal operator is not necessarily a selfdual subnormal operator, although $S$ is subnormal. In this paper we examine a pure operator $S$ of this type. We observe that this decomposition is unique. Moreover we show a necessary and sufficient condition for a subnormal operator to be of this type. This is an improvement of Brown's theorem [2] concerning quasinormal operators. We also give a necessary and sufficient condition for an operator of this type to be a selfdual subnormal operator.
AMS Subject Classification
(1991): 47B20
Received August 11, 1993. (Registered under 5577/2009.)
Abstract. In this paper the discussion of normal spectral approximation in a unital $C^*$algebra is continued. For the approximation by positive or selfadjoint elements and by positive contractions in the $C^*$norm as well as in a second norm the extreme points of the convex set of all approximants are studied. The main purpose of this paper is to develop sufficient conditions for an approximant to be such an extreme point. As an application many extreme points for the approximation of normal elements are constructed. Moreover for the approximation in the $C^*$algebra of all bounded linear operators on a complex Hilbert space the number of extreme points is completely determined.
AMS Subject Classification
(1991): 47A58
Received August 30, 1993. (Registered under 5578/2009.)
Jerzy Kąkol,
Pekka Sorjonen

161171

Abstract. The main purpose is to give necessary and sufficient conditions for a metrizable topological vector space with a generalized form of HahnBanach extension property to be locally convex and describe the Mackey envelope of such spaces.
AMS Subject Classification
(1991): 46A16, 46A22
Received September 23, 1993. (Registered under 5579/2009.)
Takahiko Nakazi,
Masahiro Yamada

173185

Abstract. Toeplitz operators $T_\phi ^M$ are defined on invariant subspaces $M$ of an arbitrary uniform algebra $A$. We give a necessary and sufficient condition for uniform invertibility of $M_\phi ^M$ with respect to some family $\cal F$ of invariant subspaces $M$. This condition is the same as a classical one in case $A$ is the disc algebra. In special uniform algebras we can choose a small family, in fact, if $A$ is a disc algebra then $\cal F$ can be a single set. Then this generalizes the WidomDevinatz Theorem. As an application, we study a $\cal F$union of spectra of $\{T_\phi ^M;M\in{\cal F}\} $.
AMS Subject Classification
(1991): 47B35, 47A10
Keyword(s):
Toeplitz operator,
invertible,
uniform algebra,
spectrum
Received November 10, 1993 and in revised form March 21, 1994. (Registered under 5580/2009.)
In Ho Jeon,
Woo Young Lee

187193

Abstract. In this note we discuss the TaylorWeyl spectrum of a commuting pair of operators acting on a Hilbert space and compare the TaylorWeyl spectrum with a joint Weyl spectrum due to Chō and Takaguchi.
AMS Subject Classification
(1991): 47A13, 47A10, 47A53
Received December 20, 1993 and in revised form March 25, 1994. (Registered under 5581/2009.)
Tingfu Wang,
Zhongrui Shi,
Guanghai Chen

195208

Abstract. By giving the sufficient and necessary condition of URED for Orlicz sequence spaces endowed with Orlicz norm, we solve the open problem posed in [3].
AMS Subject Classification
(1991): 46E30
Keyword(s):
Orlicz sequence space,
uniform rotundity in every direction
Received January 6, 1992 and in revised from May 21, 1993. (Registered under 5582/2009.)
L. Leindler,
A. Meir

209220

Abstract. We prove two general theorems. Applying these results we also prove certain ``converses'' of four theorems proved by the first author earlier. It is also verified that the new results, in general, can not be substantially improved.
AMS Subject Classification
(1991): 40A05, 40A10, 40A99
Received April 19, 1993. (Registered under 5583/2009.)
Jöran Bergh,
Victor Burenkov,
Lars Erik Persson

221239

Abstract. If we consider the class of (quasi)monotone functions, then Hardy's classical inequalities hold also in the reversed direction for {\it some} constants. In this paper we present several proofs of these reversed Hardy's inequalities, which, in particular, give the best possible constants in all cases. The results obtained may be regarded as a unification and generalization of some results recently obtained in [2], [4] and [11].
AMS Subject Classification
(1991): 26D15, 26D20
Received April 19, 1993. (Registered under 5584/2009.)
W. B. Jurkat,
D. J. F. Nonnenmacher

241256

Abstract. Applying a recently developed axiomatic theory of nonabsolutely convergent integrals we define a relatively simple and wellbehaved integral over $n$dimensional compact intervals for which the divergence theorem holds in its presently most general form.
AMS Subject Classification
(1991): 26A39, 26B20
Received April 23, 1993. (Registered under 5585/2009.)
Dang Vu Giang,
Ferenc Móricz

257265

Abstract. We show that if a function $f$ defined on the real line ${\bf R}$ belongs to the Besov space $B^{1/p}_{p,1},$ where $1\le p< \infty,$ then its Dirichlet integral $s_T(f,x)$ converges uniformly as $T\to\infty.$ In the case where $1\le p\le2$, we even prove that $s_T(f,x)$ converges absolutely. It follows easily that any function $f$ in $B^{1/p}_{p,1}, 1\le p\le2,$ is a Fourier transform on $L^1({\bf R}).$ The counterparts of our results were proved by A. M. Garsia (1976) for functions defined on the unit circle ${\bf T}.$ Our proofs are basically different from those given there.
AMS Subject Classification
(1991): 42A38, 46E35, 41A17
Keyword(s):
Besov space,
modulus of continuity,
Fourier transform,
Dirichlet integral,
Riesz mean,
HardyLittlewood inequality,
L^1.,
multiplier of Fourier transform on
Received September 15, 1993. (Registered under 5586/2009.)
Younhee Ko

267278
No further details

Abstract. In this paper we define and study exposed points of subsets in a smooth Riemannian manifold without focal points. Sectional curvature at exposed points is studied. Proofs of wellknown theorems are given as corollaries of the established results.
AMS Subject Classification
(1991): 53C42
Keyword(s):
Manifolds without focal points,
convex subsets,
geodesics,
sectional curvature
Received June 10, 1993 and in revised form November 24, 1993. (Registered under 5588/2009.)

289317
No further details

