Local behaviour of the polynomial calculus of operators.
On domination and extensions of Banach algebras
The splitting spectrum differs from the Taylor spectrum
We construct a pair of commuting Banach space operators for which the splitting spectrum is different from the Taylor spectrum.
On topologizable algebras
Non-removable ideals in commutative Banach algebras
On the Taylor functional calculus
We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.
Vasilescu-Martinelli formula for operators in Banach spaces
We prove a formula for the Taylor functional calculus for functions analytic in a neighbourhood of the splitting spectrum of an n-tuple of commuting Banach space operators. This generalizes the formula of Vasilescu for Hilbert space operators and is closely related to a recent result of D. W. Albrecht.
A note on topologically nilpotent Banach algebras
A Banach algebra A is said to be topologically nilpotent if tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]
On the axiomatic theory of spectrum
There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).
A quasi-nilpotent operator with reflexive commutant, II
A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. The norms converge to zero arbitrarily fast.
On the axiomatic theory of spectrum II
We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.
Open set of eigenvalues and SVEP
On Ulam's hypothesis
Stability of infinite ranges and kernels
Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces and do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.
Corrigendum and addendum: "On the axiomatic theory of spectrum II"
The main purpose of this paper is to correct the proof of Theorem 15 of [4], concerned with the stability of the class of quasi-Fredholm operators under finite rank perturbations, and to answer some open questions raised there.
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