ACTA issues

Deddens algebras and weighted shifts of infinite multiplicity

Srdjan Petrovic, Daniel Sievewright

Acta Sci. Math. (Szeged) 82:3-4(2016), 577-595

Abstract. We consider the weighted shifts of infinite multiplicity with quasi-affine weights. We obtain a necessary and sufficient condition for the Deddens algebra associated to such a shift to have a nontrivial invariant subspace, or to be dense. Our technique is based on the study of compressions of operators in the Deddens algebra to some subspaces, and the relations between such compressions.

DOI: 10.14232/actasm-014-789-3

AMS Subject Classification (1991): 47A15, 47B37

Keyword(s): Deddens algebra, weighted shift, invariant subspace

Received May 6, 2014, and in final form June 23, 2016. (Registered under 39/2014.)