School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Article

Publication Date

11-28-2020

Abstract

Given a pair of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair of normal extensions of and ; in other words, is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift is subnormal, then is subnormal if and only if a power is subnormal for some . As a corollary, we have that if is a 2-variable weighted shift having a tensor core or a diagonal core, then is subnormal if and only if a power of is subnormal.

Comments

Copyright © 2020 Sang Hoon Lee et al.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Function Spaces

DOI

10.1155/2020/5678795

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 1
  • Usage
    • Downloads: 133
    • Abstract Views: 5
see details

Included in

Mathematics Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.