Multiplicities, invariant subspaces and an additive formula
Proceedings of the Edinburgh Mathematical Society
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.
Chattopadhyay, Arup; Sarkar, Jaydeb; and Sarkar, Srijan, "Multiplicities, invariant subspaces and an additive formula" (2021). Journal Articles. 1977.
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