$q$-Berezin Range of Operators in Hardy Space
Debarati Bhattacharya, Arnab Patra
TL;DR
This paper explores the $q$-Berezin range and number of operators on Hardy space, analyzing their properties and convexity for various classes of operators.
Contribution
It introduces the concept of the $q$-Berezin range for operators on Hardy space and studies its convexity for specific operator classes.
Findings
Determined the $q$-Berezin range for certain classes of operators.
Established convexity of the $q$-Berezin range for finite-rank, diagonal, and other operators.
Extended the understanding of $q$-Berezin concepts in Hardy space context.
Abstract
This paper investigates the concept of the -Berezin range and -Berezin number of bounded linear operators acting on Hardy space. We obtain the -Berezin range of some classes of operators on Hardy space. In addition, the convexity of the -Berezin range is explored for finite-rank, diagonal, multiplication, weighted shift, and certain composition operators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.