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Inessential operators and incomparability of Banach spaces.

Pietro Aiena, Manuel González (1991)

Extracta Mathematicae

We obtain several characterizations for the classes of Riesz and inessential operators, and apply them to extend the family of Banach spaces for which the essential incomparability class is known, solving partially a problem posed in [6].

Linear inessential operators and generalized inverses

Bruce A. Barnes (2009)

Commentationes Mathematicae Universitatis Carolinae

The space of inessential bounded linear operators from one Banach space X into another Y is introduced. This space, I ( X , Y ) , is a subspace of B ( X , Y ) which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces W of I ( X , Y ) , it is shown that when T ∈ B ( X , Y ) has a generalized inverse modulo W , then there exists a projection P ∈ B ( X ) such that T ( I - P ) has a generalized inverse and T P ∈ W .

On a formula for the jumps in the semi-Fredholm domain.

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.

On a Weyl-von Neumann type theorem for antilinear self-adjoint operators

Santtu Ruotsalainen (2012)

Studia Mathematica

Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed....

On an estimate for the norm of a function of a quasihermitian operator

M. Gil (1992)

Studia Mathematica

Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator A p - ( A * ) p is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.

On generalized a-Browder's theorem

Pietro Aiena, T. Len Miller (2007)

Studia Mathematica

We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.

On generalized property (v) for bounded linear operators

J. Sanabria, C. Carpintero, E. Rosas, O. García (2012)

Studia Mathematica

An operator T acting on a Banach space X has property (gw) if σ a ( T ) ∖ σ S B F ₊ ¯ ( T ) = E ( T ) , where σ a ( T ) is the approximate point spectrum of T, σ S B F ₊ ¯ ( T ) is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and σ ( T ) = σ a ( T ) .

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