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...