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An amalgamation of the Banach spaces associated with James and Schreier, Part II: Banach-algebra structure

Alistair Bird (2010)

Banach Center Publications

The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.

Approximate and weak amenability of certain Banach algebras

P. Bharucha, R. J. Loy (2010)

Studia Mathematica

The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for ℓ p -sums of finite-dimensional normed algebras.

Arens regularity of module actions

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual ( n ) of . Banach algebras for which Z( **) = but ⊊ Z t ( * * ) are...

Character Connes amenability of dual Banach algebras

Mohammad Ramezanpour (2018)

Czechoslovak Mathematical Journal

We study the notion of character Connes amenability of dual Banach algebras and show that if A is an Arens regular Banach algebra, then A * * is character Connes amenable if and only if A is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras....

Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani, Sima Soltani Renani (2011)

Studia Mathematica

Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Character inner amenability of certain Banach algebras

H. R. Ebrahimi Vishki, A. R. Khoddami (2011)

Colloquium Mathematicae

Character inner amenability for a certain class of Banach algebras including projective tensor products, Lau products and module extensions is investigated. Some illuminating examples are given.

Character pseudo-amenability of Banach algebras

Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.

Commutative, radical amenable Banach algebras

C. Read (2000)

Studia Mathematica

There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector y 1 ; then approximate...

Compactness of derivations from commutative Banach algebras

Matthew J. Heath (2010)

Banach Center Publications

We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give...

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