The (U + K)-Orbit of Essentially Normal Operators and Compact Perturbation of Strongly Irreducible Operators

1996 ◽  
pp. 307-314
Author(s):  
Youqing Ji ◽  
Chunlan Jiang ◽  
Zhongyao Wang
Keyword(s):  
Compact Perturbation ◽  
Strongly Irreducible Operators ◽  
Essentially Normal ◽  
Strongly Irreducible ◽  
Normal Operators

Hyponormal and essentially normal operators

1979 ◽  
Vol 83 (1-2) ◽  
pp. 123-132
Author(s):  
C. R. Putnam
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Principal Result ◽  
Hyponormal Operator ◽  
Essentially Normal ◽  
Normal Operators ◽  
Result Theorem ◽  
Almost All ◽  
Spectral Family

SynopsisLet 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.

scholarly journals Restrictions of essentially normal operators

1990 ◽  
Vol 20 (2) ◽  
pp. 613-618
Author(s):  
L. WILLIAMS
Keyword(s):  
Essentially Normal ◽  
Normal Operators
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