Invariant subspaces of analytic perturbations

2021/07/11 by Das, Susmita, Sarkar, Jaydeb · 1 citation
#30H10 #30J05 #46E22 #47A15 #47A55 #47B20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2107.05052

Abstract

By analytic perturbations, we refer to shifts that are finite rank perturbations of the form M_z + F, where M_z is the unilateral shift and F is a finite rank operator on the Hardy space over the open unit disc. Here shift refers to the multiplication operator M_z on some analytic reproducing kernel Hilbert space. In this paper, we first isolate a natural class of finite rank operators for which the corresponding perturbations are analytic, and then we present a complete classification of invariant subspaces of those analytic perturbations. We also exhibit some instructive examples and point out several distinctive properties (like cyclicity, essential normality, hyponormality, etc.) of analytic perturbations.

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