Reductive algebras containing a direct sum of the unilateral shift and a certain other operator are selfadjoint

Author:
Mohamad A. Ansari

Journal:
Proc. Amer. Math. Soc. **93** (1985), 284-286

MSC:
Primary 47C15; Secondary 46L10, 47D25

DOI:
https://doi.org/10.1090/S0002-9939-1985-0770537-6

MathSciNet review:
770537

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Abstract: We give a partial solution of the reductive algebra problem to prove that: a reductive algebra containing the direct sum of a unilateral shift of finite multiplicity and a finite-dimensional completely nonunitary contraction is a von Neumann algebra.

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0770537-6

Article copyright:
© Copyright 1985
American Mathematical Society