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Search: MSC category 46H20 ( Structure, classification of topological algebras )

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1. CMB 2016 (vol 60 pp. 122)

Ghanei, Mohammad Reza; Nasr-Isfahani, Rasoul; Nemati, Mehdi
A Homological Property and Arens Regularity of Locally Compact Quantum Groups
We characterize two important notions of amenability and compactness of a locally compact quantum group ${\mathbb G}$ in terms of certain homological properties. For this, we show that ${\mathbb G}$ is character amenable if and only if it is both amenable and co-amenable. We finally apply our results to Arens regularity problems of the quantum group algebra $L^1({\mathbb G})$; in particular, we improve an interesting result by Hu, Neufang and Ruan.

Keywords:amenability, Arens regularity, co-amenability, locally compact quantum group, homological property
Categories:46L89, 43A07, 46H20, 46M10, 58B32

2. CMB 2014 (vol 58 pp. 3)

Alaghmandan, Mahmood
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

3. 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

4. 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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