School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A new characterization of subnormality for a class of 2-variable weighted shifts with 1-atomic core

Document Type

Article

Publication Date

2-2018

Abstract

Given a pair T≡(T1,T2) of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) calls for necessary and sufficient conditions for the existence of a commuting pair N≡(N1,N2) of normal extensions of T1 and T2 . This is an old problem in operator theory. The aim of this paper is to study LPCS. There are three well-known subnormal characterizations for operators: the Berger Theorem, the Bram–Halmos characterization, and Franks' result. In our paper, we study a new subnormal characterization which is related to these three well-known ones for a class of 2-variable weighted shifts. Thus, we can provide a large nontrivial class of 2-variable weighted shifts in which k-hyponormal (some k≥1 ) and subnormal are equal and the class is invariant under the action (h,ℓ)↦T(h,ℓ):=(T h 1 ,T ℓ 2 ) (h,ℓ≥1 ).

Comments

Under an Elsevier user license

Publication Title

Linear Algebra and its Applications

DOI

10.1016/j.laa.2017.10.010

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