Related papers: Why Banach algebras?
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 discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering of the unit ball.
We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…
It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…
Properties of the inverse along an element in rings with an involution, Banach algebras and $C^*$-alegbras will be studied unifying known expressions concerning generalized inverses.
The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…
In this paper, we introduce the concept of the generalized right group inverse within the context of a *-Banach algebra. This represents a natural extension of the generalized (weak) group inverse. Notably, this generalized inverse is…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
We introduce the concept of an $E$-valued function algebra, a type of Banach algebra that consist of continuous $E$-valued functions on some compact Hausdorff space, where $E$ is a Banach algebra. We present some basic results about such…
In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.
We study properties of representing and absolutely representing systems of subspaces in Banach spaces. We also present sufficient conditions for the system of subspaces to be a representing system of subspaces.
Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for…
In this paper, we study multiplicative weak convergence in Banach f-algebra and multiplicative weak* convergence in its dual.
We generalize the notion of flat chains with arbitrary coefficient groups to Banach spaces and prove a sequential compactness result. We also remove the restriction that a flat chain have finite mass in order for its support to exist.
We initiate the study of cortex algebras (commutative Banach algebras with extendable multiplicative-linear functionals) and the spectral permanence property. In addition, we analyze some particular examples in this context and present open…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.