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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
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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Article copyright: © Copyright 1985 American Mathematical Society

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