Tensor products of subnormal operators

Author:
Nathan S. Feldman

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2685-2695

MSC (1991):
Primary 47B20; Secondary 47A80

DOI:
https://doi.org/10.1090/S0002-9939-99-05054-6

Published electronically:
April 9, 1999

MathSciNet review:
1625745

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Abstract | References | Similar Articles | Additional Information

Abstract: We shall use a -algebra approach to study operators of the form where is subnormal and is normal. We shall determine the spectral properties for these operators, and find the minimal normal extension and the dual operator. We also give a necessary condition for to contain a compact operator and a sufficient condition for the algebraic equivalence of and .

We also consider the existence of a homomorphism satisfying . We shall characterize the operators such that exists for every operator .

The problem of when is unitarily equivalent to is considered. Complete results are given when and are positive operators with finite multiplicity functions and has compact self-commutator. Some examples are also given.

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Additional Information

**Nathan S. Feldman**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

Email:
feldman@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05054-6

Keywords:
Tensor product,
subnormal operator,
dual operator

Received by editor(s):
November 20, 1997

Published electronically:
April 9, 1999

Additional Notes:
This paper was written while the author was a graduate student at the University of Tennessee working under the direction of Professor John B. Conway. He received partial support from the NSF grant DMS–9401027.

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society