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Proceedings of the American Mathematical Society

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Compact operators in the algebra generated by essentially unitary $ C\sb{0}$ operators


Author: Eric A. Nordgren
Journal: Proc. Amer. Math. Soc. 51 (1975), 159-162
MSC: Primary 47A15; Secondary 46L15, 47C05
DOI: https://doi.org/10.1090/S0002-9939-1975-0370222-2
MathSciNet review: 0370222
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Abstract: It will be shown that the compact operators in the weakly closed algebra generated by an essentially unitary $ {C_0}$ contraction are weakly dense in the algebra. The result implies the extension of a double dual theorem of Kriete, Moore and Page and yields a partial answer to a question on reductive algebras raised by Rosenthal.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0370222-2
Keywords: Hilbert space operator, $ {C_0}$ contraction, compact defect operator, reductive algebra
Article copyright: © Copyright 1975 American Mathematical Society