Related papers: Derivations preserving quasinilpotent elements

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

The main results of the paper: {\bf (1)} The dual Banach space $X^*$ contains a linear subspace $A\subset X^*$ such that the set $A^{(1)}$ of all limits of weak$^*$ convergent bounded nets in $A$ is a proper norm-dense subset of $X^*$ if…

For locally convex, nilpotent Lie algebras we construct faithful representations by nilpotent operators on a suitable locally convex space. In the special case of nilpotent Banach-Lie algebras we get norm continuous representations by…

Let $A$ and $B$ be complex unital Banach algebras, and let $\varphi, \psi: A \to B$ be surjective mappings. If $A$ is semisimple with an essential socle and $\varphi$ and $\psi$ preserves the invertibility of linear pencils in both…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…

We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show…

We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…

In this paper, we show that the essentiality of the scole of an ideal B i a semi-simple Banach algebra A implies that any invertibility preserving isomorphism on A is a Jordan homomorphism. Specially ...

Let $X$ be a perfect, compact subset of the complex plane. We consider algebras of those functions on $X$ which satisfy a generalised notion of differentiability, which we call $\mathcal{F}$-differentiability. In particular, we investigate…

We initiate the large scale geometric study of Banach-Lie groups, especially of linear Banach-Lie groups. We show that the exponential length, originally introduced by Ringrose for unitary groups of $C^*$-algebras, defines the…

Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and…

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X of dimension at least three. For an arbitrary nonzero complex number t we determine the form of mappings f: B(X)-->B(X) with sufficiently large range such…

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and…

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 unital Banach algebra that cannot be realised as a~Calkin…

We construct a crossed product Banach algebra from a Banach algebra dynamical system $(A,G,\alpha)$ and a given uniformly bounded class $R$ of continuous covariant Banach space representations of that system. If $A$ has a bounded left…

We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach…

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case.…

It is a well-known fact in K-theory that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion map is continuous. We…

A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an…

We prove that given a locally compact Hausdorff space, $K$, and a compact C$^*$-algebra, $\mathcal{A}$, the C$^*$-algebra $C(K, \mathcal{A})$ satisfies that every convex combination of slices of the closed unit ball is relatively weakly…