Some thoughts on composition operators on subspaces of the Hardy space

Anand, J and Bhattacharyya, T and Srivastava, S (2020) Some thoughts on composition operators on subspaces of the Hardy space. In: Archiv der Mathematik, 114 (4). pp. 431-444.

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Abstract

We discuss composition operators on certain subspaces of the Hardy space. The family of subspaces that we deal with are called Hα,β2 which have garnered a lot of attention recently for results related to interpolation. We use them effectively here to study composition operators. Three aspects are discussed. The first is invariance. We examine when Hα,β2 or JHα,β2 where J is an inner function are left invariant by composition operators. Secondly, we show that for detecting whether a function φ is inner or not, the composition operator with the symbol φ can be used efficiently on certain subspaces. Thirdly, we discover a criterion for detecting invertibility in the footsteps of the classical result of Schwartz

Item Type:	Journal Article
Publication:	Archiv der Mathematik
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to the Birkhauser.
Keywords:	Composition operators; Inner functions; Invariant subspaces
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Feb 2023 08:59
Last Modified:	01 Feb 2023 08:59
URI:	https://eprints.iisc.ac.in/id/eprint/79674

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