Inner invariant extensions of Dirac measures on compactly cancellative topological semigroups

Bami, M. Lashkarizadeh ; Mohammadzadeh, B. ; Nasr-Isfahani, R.

Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 699-708 / Harvested from Project Euclid

Résumé

Let ${\cal S}$ be a left compactly cancellative foundation semigroup with identity $e$ and $M_a({\cal S})$ be its semigroup algebra. In this paper, we give a characterization for the existence of an inner invariant extension of $\delta_e$ from $C_b({\cal S})$ to a mean on $L^\infty({\cal S},M_a({\cal S}))$ in terms of asymptotically central bounded approximate identities in $M_a({\cal S})$. We also consider topological inner invariant means on $L^\infty({\cal S},M_a({\cal S}))$ to study strict inner amenability of $M_a({\cal S})$ and their relation with strict inner amenability of ${\cal S}$.

Détail

Publié le : 2007-11-14
Classification:  Inner invariance,  inner invariant extension,  mixed identity,  strict inner amenability,  topological inner invariance,  43A07,  43A10,  43A15,  46H05