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- Title
DISTINGUISHED SUBSPACES OF TOPELITZ OPERATORS ON N<sub>ϕ</sub> -TYPE QUOTIENT MODULES.
- Authors
HONG ZOU; TAO YU
- Abstract
In this paper, we show that there always exists reducing subspace M for Sψ(z) such that the restriction of Sψ(z) on M is unitarily equivalent to the Bergman shift when ψ(z) is a finite Blaschke product. Moreover, we will show that only if ψ(z) is a finite Blaschke product can Sψ(z) has distinguished reducing subspaces. We also give the form of these distinguished reducing subspaces when ψ(z) is a finite Blaschke product. Finally, we show that every nontrivial minimal reducing subspace S of Sψ(z) is orthogonal to the direct sum of all distinguished subspaces when S is not a distinguished subspace of Sψ(z).
- Subjects
OPERATOR theory; MODULES (Algebra); SUBSPACES (Mathematics); BLASCHKE products; SET theory
- Publication
Operators & Matrices, 2022, Vol 16, Issue 2, p279
- ISSN
1846-3886
- Publication type
Article
- DOI
10.7153/oam-2022-16-22