The orbit of a bounded operator under the Möbius group modulo similarity equivalence

Ghara, S (2020) The orbit of a bounded operator under the Möbius group modulo similarity equivalence. In: Israel Journal of Mathematics, 238 (1). pp. 167-207.

PDF ISR_JOU_MAT_238_1_167-207_2020.pdf - Published Version Restricted to Registered users only Download (362kB) | Request a copy

Abstract

Let Möb denote the group of biholomorphic automorphisms of the unit disc and (Möb · T) be the orbit of a Hilbert space operator T under the action of Möb. If the quotient InlineMediaObject not available: see fulltext., where InlineMediaObject not available: see fulltext. is the similarity between two operators is a singleton, then the operator T is said to be weakly homogeneous. In this paper, we obtain a criterion to determine if the operator Mz of multiplication by the coordinate function z on a reproducing kernel Hilbert space is weakly homogeneous. We use this to show that there exists a Möbius bounded weakly homogeneous operator which is not similar to any homogeneous operator, answering a question of Bagchi and Misra in the negative. Some necessary conditions for the Möbius boundedness of a weighted shift are also obtained. As a consequence, it is shown that the Dirichlet shift is not Möbius bounded. © 2020, The Hebrew University of Jerusalem.

Item Type:	Journal Article
Publication:	Israel Journal of Mathematics
Publisher:	Hebrew University Magnes Press
Additional Information:	Copy right for this article belongs to Hebrew University Magnes Press
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	20 Nov 2020 11:37
Last Modified:	20 Nov 2020 11:37
URI:	http://eprints.iisc.ac.in/id/eprint/65638

Actions (login required)

View Item