The (u+κ)-orbit of essentially normal operators and compact perturbations of strongly irreducible operators-orbit of essentially normal operators and compact perturbations of strongly irreducible operators

2000 ◽  
Vol 21 (2) ◽  
pp. 237-248
Author(s):  
Ji Youqing ◽  
Jiang Chunlan ◽  
Wang Zonyao
Keyword(s):  
Strongly Irreducible Operators ◽  
Essentially Normal ◽  
Compact Perturbations ◽  
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.

Compact perturbations of normal operators in a Krein space

1990 ◽  
Vol 42 (10) ◽  
pp. 1155-1161 ◽  
Author(s):  
T. Ya. Azizov ◽  
P. Ionas
Keyword(s):  
Krein Space ◽  
Compact Perturbations ◽  
Kreĭn Space ◽  
Normal Operators
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