7 citations · 24 across the 11 of their papers we have counts for
11 papers · 1 filter
Twisting exponential spectra
Bence Horváth, Tomasz Kania
Klaja and Ransford exhibited a complex unital Banach algebra in which the exponential spectra of \(ab\) and \(ba\) differ away from zero, and asked whether this can occur in an alg…
Pure infiniteness and primary factorisation
Antonio Acuaviva, Bence Horváth, Tomasz Kania
We show that there is no real or complex indecomposable Banach space with the primary factorisation property (PFP). We relate the PFP of a Banach space to ring-theoretic infini…
Kernels of operators on Banach spaces induced by almost disjoint families
Bence Horváth, Niels Jakob Laustsen
Let~ be an almost disjoint family of subsets of an infinite set~, and denote by~ the closed subspace of~ spanned by the indicator f…
Approximately multiplicative maps between algebras of bounded operators on Banach spaces
Yemon Choi, Bence Horváth, Niels Jakob Laustsen
We show that for any separable reflexive Banach space and a large class of Banach spaces , including those with a subsymmetric shrinking basis but also all spaces for…
A purely infinite Cuntz-like Banach -algebra with no purely infinite ultrapowers
Matthew Daws, Bence Horváth
We continue our investigation, from \cite{dh}, of the ring-theoretic infiniteness properties of ultrapowers of Banach algebras, studying in this paper the notion of being purely in…
Unital Banach algebras not isomorphic to Calkin algebras of separable Banach spaces
Bence Horváth, Tomasz Kania
Recent developments in Banach space theory provided unexpected examples of unital Banach algebras that are isomorphic to Calkin algebras of Banach spaces, however no example of a u…
Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective
Bence Horváth, Tomasz Kania
We study automatic injectivity of surjective algebra homomorphisms from , the algebra of (bounded, linear) operators on , to , where is one o…
Perturbations of surjective homomorphisms between algebras of operators on Banach spaces
Bence Horváth, Zsigmond Tarcsay
A remarkable result of Molnár [Proc. Amer. Math. Soc., 126 (1998), 853-861] states that automorphisms of the algebra of operators acting on a separable Hilbert space is stable unde…
Ring-theoretic (in)finiteness in reduced products of Banach algebras
Matthew Daws, Bence Horváth
We study ring-theoretic (in)finiteness properties -- such as \emph{Dedekind-finiteness} and \emph{proper infiniteness} -- of ultraproducts (and more generally, reduced products) of…
When are full representations of algebras of operators on Banach spaces automatically faithful?
Bence Horváth
We examine the phenomenon when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we shall…
A Banach space whose algebra of operators is Dedekind-finite but it does not have stable rank one
Bence Horváth
In this note we examine the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space . We show that for the indecomposab…