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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasi-similarity of weak contractions


Author: Pei Yuan Wu
Journal: Proc. Amer. Math. Soc. 69 (1978), 277-282
MSC: Primary 47A45
MathSciNet review: 0482302
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Abstract: Let T be a completely nonunitary (c.n.u.) weak contraction (in the sense of Sz.-Nagy and Foiaş). We show that T is quasi-similar to the direct sum of its $ {C_0}$ part and $ {C_{11}}$ part. As a corollary, two c.n.u. weak contractions are quasi-similar to each other if and only if their $ {C_0}$ parts and $ {C_{11}}$ parts are quasi-similar to each other, respectively. We also completely determine when c.n.u. weak contractions and $ {C_0}$ contractions are quasi-similar to normal operators.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0482302-4
PII: S 0002-9939(1978)0482302-4
Keywords: Completely nonunitary weak contractions, quasi-similarity, $ {C_0}$ parts, $ {C_{11}}$ parts, normal operators
Article copyright: © Copyright 1978 American Mathematical Society