Displaying similar documents to “Fredholm theory in Banach algebras”

On regularities and Fredholm theory

L. Lindeboom, H. Raubenheimer (2002)

Czechoslovak Mathematical Journal

Similarity:

We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.

The index for Fredholm elements in a Banach algebra via a trace II

Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz (2016)

Czechoslovak Mathematical Journal

Similarity:

We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.

The index for Fredholm elements in a Banach algebra via a trace

J. J. Grobler, H. Raubenheimer (2008)

Studia Mathematica

Similarity:

We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.

An Atkinson-type theorem for B-Fredholm operators

M. Berkani, M. Sarih (2001)

Studia Mathematica

Similarity:

Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only...

Fredholm multipliers of semisimple commutative Banach algebras.

Pietro Aiena (1991)

Extracta Mathematicae

Similarity:

In some recent papers ([1],[2],[3],[4]) we have investigated some general spectral properties of a multiplier defined on a commutative semi-simple Banach algebra. In this paper we expose some aspects concerning the Fredholm theory of multipliers.

Operational quantities derived from the norm and generalized Fredholm theory.

Manuel González, Antonio Martinón (1991)

Extracta Mathematicae

Similarity:

Several operational quantities, defined in terms of the norm and the class of finite dimensional Banach spaces, have been used to characterize the classes of upper and lower semi-Fredholm operators, strictly singular and strictly cosingular operators, and to derive some perturbation results. In this paper we shall introduce and study some operational quantities derived from the norm and associated to a space ideal. By means of these quantities we construct a generalized...