Normed algebras with involution.
The Słodkowski spectra and higher Shilov boundaries
We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
Local behaviour of operators
Nil, nilpotent and PI-algebras
The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in the literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. However, even this work has not get so much attention as it deserves. The present paper...
On the joint spectral radius
We prove the -spectral radius formula for n-tuples of commuting Banach algebra elements
On Jordan models of -contractions
Axiomatic theory of spectrum III: semiregularities
We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).
Inverse elements in extensions of Banach algebras
Removability of ideals in commutative Banach algebras
Adjoining inverses to noncommutative Banach algebras and extensions of operators
The joint essential numerical range, compact perturbations, and the Olsen problem
Let T₁,...,Tₙ be bounded linear operators on a complex Hilbert space H. Then there are compact operators K₁,...,Kₙ ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T₁-K₁,...,Tₙ-Kₙ) equals the joint essential numerical range of (T₁,...,Tₙ). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ ℕ then there exists a compact operator K ∈ B(H) such that . This generalizes results of C. L. Olsen.
Embeddings of separable Banach star algebras into a Banach star algebra with one generator.
Non-removable ideals in commutative topological algebras with separately continuous multiplication.
An ideal in a commutative topological algebra with separately continuous multiplication is non-removable if and only if it consists locally of joint topological divisors of zero. Also, any family of non-removable ideals can be removed simultanously.
Poznámky k experimentálnímu studiu fysikálních vlastností vulkanisátů kaučuku
On domination problem in Banach algebras
Non-removable ideals in commutative Banach algebras
On the topological boundary of the one-sided spectrum
It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.
A note on joint capacities in Banach algebras
A note on the joint spectrum in commutative Banach algebras
Probabilistic reconstruction from subgraphs
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