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Invariant subspaces in the bidisc and commutators

Part of: Special classes of linear operators Commutative Banach algebras and commutative topological algebras Holomorphic functions of several complex variables General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan
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Abstract

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Let M be an invariant subspace of L2 (T2) on the bidisc. V1 and V2 denote the multiplication operators on M by coordinate functions z and ω, respectively. In this paper we study the relation between M and the commutator of V1 and , For example, M is studied when the commutator is self-adjoint or of finite rank.

MSC classification

Secondary: 47A15: Invariant subspaces 47B47: Commutators, derivations, elementary operators, etc. 47B20: Subnormal operators, hyponormal operators, etc. 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces 32A35: $H^p$-spaces, Nevanlinna spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 2 , April 1994 , pp. 232 - 242
Copyright
Copyright © Australian Mathematical Society 1994

References

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