Multiplicities, invariant subspaces and an additive formula

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

This document is currently not available here.

Share

COinS