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Metric version of flatness and Hahn-Banach type theorems for normed modules over sequence algebras

A. Ya. Helemskii (2011)

Studia Mathematica

We introduce and study the metric or extreme versions of the notions of a flat and an injective normed module. The relevant definitions, in contrast with the standard known ones, take into account the exact value of the norm of the module. The main result gives a full characterization of extremely flat objects within a certain category of normed modules. As a corollary, some Hahn-Banach type theorems for normed modules are obtained.

Module Connes amenability of hypergroup measure algebras

Massoud Amini (2015)

Open Mathematics

We define the concept of module Connes amenability for dual Banach algebras which are also Banach modules with a compatible action. We distinguish a closed subhypergroup K0 of a locally compact measured hypergroup K, and show that, under different actions, amenability of K, M.K0/-module Connes amenability of M.K/, and existence of a normal M.K0/-module virtual diagonal are related.

Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

E., Jr. Makai, Jaroslav Zemánek (2016)

Czechoslovak Mathematical Journal

Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C * -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C * -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the...

Nil, nilpotent and PI-algebras

Vladimír Müller (1994)

Banach Center Publications

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...

(Non-)amenability of ℬ(E)

Volker Runde (2010)

Banach Center Publications

In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that ℬ ( E ) = ( E ) + ℂ i d E . Still, ℬ(ℓ²) is not amenable,...

Old and new results on Allan's GB*-algebras

Maria Fragoulopoulou, Atsushi Inoue, Klaus-Detlef Kürsten (2010)

Banach Center Publications

This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication...

On character amenable Banach algebras

Z. Hu, M. Sangani Monfared, T. Traynor (2009)

Studia Mathematica

We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...

On Gelfand-Mazur theorem on a class of F -algebras

E. Anjidani (2014)

Topological Algebra and its Applications

A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization of...

On Local Uniform Topological Algebras

Oukhouya, Ali (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.Every unital "combinatorially regular" commutative uniform complete locally m-convex algebra is local.

Currently displaying 61 – 80 of 129