Abstract. Regular subspaces are tensor products of subspaces. The structure of regular subspaces that are invariant or reducing for the tensor product of a finite collection of Hilbert space operators is entirely characterized. Necessary and sufficient conditions for a multiple tensor product of operators to be a unilateral shift are established, and it is proved that a multiple tensor product of operators is a completely nonunitary contraction if and only if each factor is a contraction, one of them being completely nonunitary.
AMS Subject Classification
(1991): 47A80, 47A15
Keyword(s):
tensor product,
Hilbert space operators,
invariant subspaces
Received October 1, 2008, and in final form April 8, 2009. (Registered under 6435/2009.)
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