Multiplicities, invariant subspaces and an additive formula

Authors

Arup Chattopadhyay, Indian Institute of Technology Guwahati
Jaydeb Sarkar, Indian Statistical Institute Bangalore
Srijan Sarkar, Indian Institute of Science

Article Type

Research Article

Publication Title

Proceedings of the Edinburgh Mathematical Society

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.

First Page

279

Last Page

297

DOI

10.1017/S0013091521000146

Publication Date

5-1-2021

Comments

Open Access, Green

Recommended Citation

Chattopadhyay, Arup; Sarkar, Jaydeb; and Sarkar, Srijan, "Multiplicities, invariant subspaces and an additive formula" (2021). Journal Articles. 1977.
https://digitalcommons.isical.ac.in/journal-articles/1977