scholarly journals Essentially Normal Operators

2010 ◽  
pp. 209-222 ◽  
Author(s):  
Kenneth R. Davidson
Keyword(s):  
Essentially Normal ◽  
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 On the structure of polynomially normal operators

1984 ◽  
Vol 30 (1) ◽  
pp. 11-18 ◽  
Author(s):  
Fuad Kittaneh
Keyword(s):  
Compact Operator ◽  
Normal Operator ◽  
Integral Theory ◽  
Direct Integral ◽  
Direct Sum ◽  
Essentially Normal ◽  
Normal Operators

We present some results concerning the structure of polynomially normal operators. It is shown, among other things, that if Tn is normal for some n > 1, then T is quasi–similar to a direct sum of a normal operator and a compact operator and if p(T) is normal with T essentially normal, then T can be written as the sum of a normal operator and a compact operator. Utilizing the direct integral theory of operators we finally show that if p(T) is normal and T*T commutes with T + T*, then T must be normal.

Sign in / Sign up

Export Citation Format

Share Document