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Can ( p ) ever be amenable?

Matthew Daws, Volker Runde (2008)

Studia Mathematica

It is known that ( p ) is not amenable for p = 1,2,∞, but whether or not ( p ) is amenable for p ∈ (1,∞) ∖ 2 is an open problem. We show that, if ( p ) is amenable for p ∈ (1,∞), then so are ( ( p ) ) and ( ( p ) ) . Moreover, if ( ( p ) ) is amenable so is ( , ( E ) ) for any index set and for any infinite-dimensional p -space E; in particular, if ( ( p ) ) is amenable for p ∈ (1,∞), then so is ( ( p ² ) ) . We show that ( ( p ² ) ) is not amenable for p = 1,∞, but also that our methods fail us if p ∈ (1,∞). Finally, for p ∈ (1,2) and a free ultrafilter over ℕ, we exhibit...

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 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.

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...

Concerning entire functions in B 0 -algebras

W. Żelazko (1994)

Studia Mathematica

We construct a non-m-convex non-commutative B 0 -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

Constructions preserving n -weak amenability of Banach algebras

A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)

Mathematica Bohemica

A surjective bounded homomorphism fails to preserve n -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

Contractible quantum Arens-Michael algebras

Nina V. Volosova (2010)

Banach Center Publications

We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established, at the...

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