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Hyponormal and essentially normal operators†

Published online by Cambridge University Press:  14 November 2011

C. R. Putnam
C. R. Putnam
Affiliation:
Purdue University, West Lafayette, Indiana, U.S.A.
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Synopsis

Let T be a hyponormal operator on a Hilbert space, so that T*T – TT*≧ 0. Let T have the Cartesian representation T = H + iJ where H has the spectral family {Et} and suppose that EtJ − JEt is compact for almost all t on a Borei set α satisfying E(α) = I. The principal result (Theorem 3) is that under these hypotheses T must be normal. In case T is hyponormal and essentially normal some sufficient conditions are given assuring that, for a fixed t, EtJ − JEt is compact.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 123 - 132
Copyright
Copyright © Royal Society of Edinburgh 1979

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