Connes-amenability of multiplier Banach algebras

Hayati, Bahman; Amini, Massoud

Kyoto J. Math., Tome 50 (2010) no. 2, p. 41-50 / Harvested from Project Euclid

Résumé

Let $B$ be a Banach algebra with bounded approximate identity, and let $M(B)$ be its multiplier algebra. If there exists a continuous linear injection $B^{*}\rightarrow M(B)$ such that, for every $b\in B$ and every $u,v\in B^{*}$ , $\langle u,vb\rangle_{B}=\langle v,bu\rangle_{B}$ , then $M(B)$ is a dual Banach algebra and the following are equivalent: ¶ (i) $B$ is amenable; ¶ (ii) $M(B)$ is Connes amenable; ¶ (iii) $M(B)$ has a normal, virtual diagonal.

Publié le : 2010-05-15
Classification: 46H20, 46H25

@article{1271187737,
     author = {Hayati, Bahman and Amini, Massoud},
     title = {Connes-amenability of multiplier Banach algebras},
     journal = {Kyoto J. Math.},
     volume = {50},
     number = {2},
     year = {2010},
     pages = { 41-50},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1271187737}
}

Hayati, Bahman; Amini, Massoud. Connes-amenability of multiplier Banach algebras. Kyoto J. Math., Tome 50 (2010) no. 2, pp.  41-50. http://gdmltest.u-ga.fr/item/1271187737/