12 Relatively Compact Perturbations of Normal Operators

2003 ◽  
pp. 173-180
Author(s):  
Michael I. Gil’
Keyword(s):  
Compact Perturbations ◽  
Normal Operators

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

On Decomposability of Compact Perturbations of Normal Operators

1975 ◽  
Vol 27 (3) ◽  
pp. 725-735 ◽  
Author(s):  
M. Radjabalipour ◽  
H. Radjavi
Keyword(s):  
Hilbert Space ◽  
Characteristic Function ◽  
Imaginary Part ◽  
Contraction Operator ◽  
Cayley Transform ◽  
Space Operator ◽  
Schatten Class ◽  
Compact Perturbations ◽  
Normal Operators ◽  
Decomposable Operator

The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T;

A note on normal operators

1963 ◽  
Vol 59 (4) ◽  
pp. 727-729 ◽  
Author(s):  
S. J. Bernau ◽  
F. Smithies
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Adjoint Operator ◽  
Spectral Theorem ◽  
Unitary Operators ◽  
Unitary Space ◽  
Bounded Linear ◽  
Finite Dimensional ◽  
Normal Operators ◽  
Finite Dimensional Case

We recall that a bounded linear operator T in a Hilbert space or finite-dimensional unitary space is said to be normal if T commutes with its adjoint operator T*, i.e. TT* = T*T. Most of the proofs given in the literature for the spectral theorem for normal operators, even in the finite-dimensional case, appeal to the corresponding results for Hermitian or unitary operators.

scholarly journals Semi-normal operators on uniformly smooth Banach spaces

1990 ◽  
Vol 32 (3) ◽  
pp. 273-276 ◽  
Author(s):  
Muneo Chō
Keyword(s):  
Banach Space ◽  
Linear Functional ◽  
Dual Space ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear ◽  
Uniformly Smooth ◽  
Normal Operators ◽  
Uniformly Smooth Banach Spaces ◽  
The Relationship

In this paper we shall examine the relationship between the numerical ranges and the spectra for semi-normal operators on uniformly smooth spaces.Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. A linear functional F on B(X) is called state if ∥F∥ = F(I) = 1. When x ε X with ∥x∥ = 1, we denoteD(x) = {f ε X*:∥f∥ = f(x) = l}.

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