J Austral Math Soc Ser A 56 pp232--242, 1994.

Invariant Subspaces in the Bidisc and Commutators

Takahiko Nakazi

(Received 19 February 1991; revised 1 August 1991)

Abstract

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

1991 AMS Subject Classification: 47A15, 47B47, 47B20, 46J15, 32A35

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Authors

Takahiko Nakazi: Department of Mathematics, Facualty of Science, Hokkaido University, Sapporo 060, Japan.

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Last Modified: Fri Jan 10 8:53:40 2003