Remarks on Hilbert-Schmidt Perturbations of Almost — Normal Operators

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.

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Semi-normal operators on uniformly smooth Banach spaces

Glasgow Mathematical Journal ◽

10.1017/s0017089500009356 ◽

1990 ◽

Vol 32 (3) ◽

pp. 273-276 ◽

Cited By ~ 1

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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Some analytical properties of the spectra of normal operators in Hilbert spaces

Proceedings of the Japan Academy ◽

10.3792/pja/1195523590 ◽

1961 ◽

Vol 37 (9) ◽

pp. 566-570

Author(s):

Sakuji Inoue

Keyword(s):

Hilbert Spaces ◽

Analytical Properties ◽

Normal Operators

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Formally Normal Operators Having no Normal Extensions

Canadian Journal of Mathematics ◽

10.4153/cjm-1965-098-8 ◽

1965 ◽

Vol 17 ◽

pp. 1030-1040 ◽

Cited By ~ 24

Author(s):

Earl A. Coddington

Keyword(s):

Hilbert Space ◽

Linear Operator ◽

Null Space ◽

Normal Operator ◽

Closed Linear Operator ◽

Normal Operators ◽

The Given ◽

Densely Defined ◽

Made In

The domain and null space of an operator A in a Hilbert space will be denoted by and , respectively. A formally normal operatorN in is a densely defined closed (linear) operator such that , and for all A normal operator in is a formally normal operator N satisfying 35 . A study of the possibility of extending a formally normal operator N to a normal operator in the given , or in a larger Hilbert space, was made in (1).

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Some inequalities for trace class operators via a Kato’s result

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500043 ◽

2017 ◽

Vol 11 (01) ◽

pp. 1850004

Author(s):

S. S. Dragomir

Keyword(s):

Hilbert Space ◽

Power Series ◽

Trace Class ◽

Complex Hilbert Space ◽

Normal Operators ◽

Trace Class Operators ◽

Kato’S Inequality ◽

New Inequalities

By the use of the celebrated Kato’s inequality, we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space [Formula: see text] Natural applications for functions defined by power series of normal operators are given as well.

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