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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.

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Official URL: https://dx.doi.org/10.1007/s11856-020-2016-x


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

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