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Nearly invariant Brangesian subspaces

Part of: Special classes of linear operators General theory of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  07 January 2025

Arshad Khan ,
Sneh Lata Open the ORCID record for Sneh Lata [Opens in a new window]  and
Dinesh Singh Open the ORCID record for Dinesh Singh [Opens in a new window]
Arshad Khan
Affiliation:
Department of Mathematics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, UP, 201314, India e-mail: [email protected]
Sneh Lata*
Affiliation:
Department of Mathematics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, UP, 201314, India e-mail: [email protected]
Dinesh Singh
Affiliation:
Centre for Digital Sciences, O. P. Jindal Global University, Sonipat, Haryana, 131001, India e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

This article describes Hilbert spaces contractively contained in certain reproducing kernel Hilbert spaces of analytic functions on the open unit disc which are nearly invariant under division by an inner function. We extend Hitt’s theorem on nearly invariant subspaces of the backward shift operator on $H^2(\mathbb {D})$ as well as its many generalizations to the setting of de Branges spaces.

Keywords

de Branges spacesnearly invariant subspacesHardy spacesmultiplication operatorreproducing kernel Hilbert spaces

MSC classification

Primary: 47A15: Invariant subspaces
Secondary: 30H10: Hardy spaces 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 318 - 337
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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