Displaying similar documents to “Fredholm determinants and the Evans function for difference equations”

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.

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...

The geometry of Kato Grassmannians

Bogdan Bojarski, Giorgi Khimshiashvili (2005)

Open Mathematics

Similarity:

We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.

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

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

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.