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Search: All articles in the CMB digital archive with keyword amenability

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1. CMB Online first

Alaghmandan, Mahmod
Approximate amenability of Segal algebras II
We prove that every proper Segal algebra of a SIN group is not approximately amenable.

Keywords:Segal algebras, approximate amenability, SIN groups, commutative Banach algebras
Categories:46H20, 43A20

2. CMB 2013 (vol 57 pp. 449)

Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim
ZL-amenability Constants of Finite Groups with Two Character Degrees
We calculate the exact amenability constant of the centre of $\ell^1(G)$ when $G$ is one of the following classes of finite group: dihedral; extraspecial; or Frobenius with abelian complement and kernel. This is done using a formula which applies to all finite groups with two character degrees. In passing, we answer in the negative a question raised in work of the third author with Azimifard and Spronk (J. Funct. Anal. 2009).

Keywords:center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups
Categories:43A20, 20C15

3. CMB 2012 (vol 57 pp. 424)

Sołtan, Piotr M.; Viselter, Ami
A Note on Amenability of Locally Compact Quantum Groups
In this short note we introduce a notion called ``quantum injectivity'' of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of locally compact groups.

Keywords:amenability, conditional expectation, injectivity, locally compact quantum group, quantum injectivity
Categories:20G42, 22D25, 46L89

4. CMB 2011 (vol 54 pp. 654)

Forrest, Brian E.; Runde, Volker
Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm
For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$-amenable in the sense of B. E. Johnson. (We can even slightly relax the norm bounds.)

Keywords:amenability, bounded approximate identity, $cb$-multiplier norm, Fourier algebra, norm one idempotent
Categories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25

5. CMB 2003 (vol 46 pp. 632)

Runde, Volker
The Operator Amenability of Uniform Algebras
We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg: A uniform algebra equipped with its canonical, {\it i.e.}, minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

Keywords:uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space
Categories:46H20, 46H25, 46J10, 46J40, 47L25

6. CMB 2001 (vol 44 pp. 504)

Zhang, Yong
Weak Amenability of a Class of Banach Algebras
We show that, if a Banach algebra $\A$ is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of $\A$ implies the ($2m+1$)-weak amenability of $\A$ for all $m\geq 1$.

Keywords:$n$-weak amenability, left ideals, left bounded approximate identity
Categories:46H20, 46H10, 46H25

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