An index theorem for systems of difference operators on a half space
Analytic formulae for determinant systems in Banach spaces
Analytic Perturbation of Semi-Fredholm Operators.
Analyticity of a joint spectrum and a multivariable analytic Fredholm theorem. (Analyticity of a joint spectrum and a multivariable analytic Fredhom theorem.)
Approximationseigenschaft, Lifting und Kohomologie bei lokalkonvexen Produktgarben.
Ascent, descent and roots of Fredholm operators
Let T be a Fredholm operator on a Banach space. Say T is rootless if there is no bounded linear operator S and no positive integer m ≥ 2 such that . Criteria and examples of rootlessness are given. This leads to a study of ascent and descent whether finite or infinite for T with examples having infinite ascent and descent.
Ascent spectrum and essential ascent spectrum
We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued extension...
a-Weyl's theorem and perturbations
We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.
a-Weyl's theorem and the single valued extension property.
In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions...
Banach spaces with small Calkin algebras
Let X be a Banach space. Let 𝓐(X) be a closed ideal in the algebra ℒ(X) of the operators acting on X. We say that ℒ(X)/𝓐(X) is a Calkin algebra whenever the Fredholm operators on X coincide with the operators whose class in ℒ(X)/𝓐(X) is invertible. Among other examples, we have the cases in which 𝓐(X) is the ideal of compact, strictly singular, strictly cosingular and inessential operators, and some other ideals introduced as perturbation classes in Fredholm theory. Our aim is to present some...
Best Fredholm perturbation theorems
B-Fredholm and Drazin invertible operators through localized SVEP
Let be a Banach space and be a bounded linear operator on . We denote by the set of all complex such that does not have the single-valued extension property at . In this note we prove equality up to between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.
Block Toeplitz operators with frequency-modulated semi-almost periodic symbols.
Browder Riesz-Schauder theory for polynomially finite rank linear relations
We describe the Browder Riesz-Schauder theory of compact operators in Banach spaces in the context of polynomially finite rank linear relations in Banach spaces.
Browder's theorems and the spectral mapping theorem.
-algebras of operators on a half-space, II. Index theory
C0-Fredholm operators (IV).
The purpose of this paper is to develop, in the context of operators of class C0, a theory of Fredholm complexes analogous to that in [6], including an index stability result under perturbations. As a by-product, a simple proof of the additivity of the index for C0-Fredholm operators will be given.
C*-Algebras of Singular Integral operators on the line realted to singular Sturm-Liouville problems.
Calkin algebras for Banach spaces with finitely decomposable quotients
For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information on the...
Characterisations of open multivalued linear operators
The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.