Cohen–Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca–Herz algebras

Runde, Volker

doi:10.1016/j.jmaa.2006.07.007

Cited by 11 publications

(10 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The converse of this statement is proved by Forrest and Runde in [48,Theorem 2.3]. It is proved in [126] that AM (A(G)) = 1 if and only if G is abelian; the same result is established for the related algebras A p (G) in [127] whenever 1 < p < ∞. We remark that it is also shown in [48] that A(G) is weakly amenable if and only if the connected component of the identity in G is abelian.…”

Section: Recall That the Notions Of A C-amenablementioning

confidence: 77%

Banach algebras on semigroups and on their compactifications

Dales¹,

Lau²,

Strauss³

2010

Memoirs of the AMS

121

164

View full text Add to dashboard Cite

Chapter 1. Introduction Chapter 2. Banach algebras and their second duals Chapter 3. Semigroups Chapter 4. Semigroup algebras Chapter 5. Stone-Čech compactifications Chapter 6. The semigroup (βS, 2) Chapter 7. Second duals of semigroup algebras Chapter 8. Related spaces and compactifications Chapter 9. Amenability for semigroups Chapter 10. Amenability of semigroup algebras Chapter 11. Amenability and weak amenability for certain Banach algebras Chapter 12. Topological centres Chapter 13. Open problems

show abstract

Section: Recall That the Notions Of A C-amenablementioning

confidence: 77%

Banach algebras on semigroups and on their compactifications

Dales¹,

Lau²,

Strauss³

2010

Memoirs of the AMS

121

164

View full text Add to dashboard Cite

show abstract

“…(or it can be directly concluded from [27,Theorem 1.5]. ) On the other hand, for f ∈ L 1 (G 0 ), ξ ∈ E, and η ∈ E * , we have…”

Section: With Aforementioned Notations Eachmentioning

confidence: 92%

$p$-Completely bounded weighted homomorphisms on the $p$-analog of the Fourier-Stieltjes algebra

Ahmadpoor¹,

Yousefi²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Ultrapowers of Banach spaces have been used in [2] to study representations of Banach algebras and representations of groups; see also the similar ideas used in [7,31].…”

Section: Proposition 22 For a Banach Algebra A An Ultrapower (A)mentioning

confidence: 99%

Amenability of ultrapowers of Banach algebras

Daws

2009

Proceedings of the Edinburgh Mathematical Society

View full text Add to dashboard Cite

We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of A is Arens regular, and give some evidence that this is so if and only if A is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapower of a dual Banach algebra. We study how tensor products of ultrapowers behave, and apply this to study the question of when every ultrapower of A is amenable. We provide an abstract characterisation in terms of something like an approximate diagonal, and consider when every ultrapower of a C * -algebra, or a group L 1 -convolution algebra, is amenable.

show abstract

Cohen–Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca–Herz algebras

Cited by 11 publications

References 34 publications

Banach algebras on semigroups and on their compactifications

Banach algebras on semigroups and on their compactifications

$p$-Completely bounded weighted homomorphisms on the $p$-analog of the Fourier-Stieltjes algebra

Amenability of ultrapowers of Banach algebras

Contact Info

Product

Resources

About