Chattopadhyay, A and Sarkar, J and Sarkar, S (2021) Multiplicities, invariant subspaces and an additive formula. In: Proceedings of the Edinburgh Mathematical Society, 64 (2). pp. 279-297.
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Abstract
Let be a commuting tuple of bounded linear operators on a Hilbert space. The multiplicity of is the cardinality of a minimal generating set with respect to. In this paper, we establish an additive formula for multiplicities of a class of commuting tuples of operators. A special case of the main result states the following: Let, and let, be a proper closed shift co-invariant subspaces of the Dirichlet space or the Hardy space over the unit disc in. If, is a zero-based shift invariant subspace, then the multiplicity of the joint-invariant subspace of the Dirichlet space or the Hardy space over the unit polydisc in is given by A similar result holds for the Bergman space over the unit polydisc. © 2021 The Author(s). Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
| Item Type: | Journal Article |
|---|---|
| Publication: | Proceedings of the Edinburgh Mathematical Society |
| Publisher: | Cambridge University Press |
| Additional Information: | The copyright for this article belongs to Author |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 26 Jul 2021 11:01 |
| Last Modified: | 26 Jul 2021 11:01 |
| URI: | http://eprints.iisc.ac.in/id/eprint/68952 |
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