## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Inner invariant extensions of Dirac measures on compactly cancellative topological semigroups

#### Abstract

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 ${\cal S}$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 4 (2007), 699-708.

Dates
First available in Project Euclid: 15 November 2007

https://projecteuclid.org/euclid.bbms/1195157138

Digital Object Identifier
doi:10.36045/bbms/1195157138

Mathematical Reviews number (MathSciNet)
MR2384465

Zentralblatt MATH identifier
1141.43001

#### Citation

Bami, M. Lashkarizadeh; Mohammadzadeh, B.; Nasr-Isfahani, R. Inner invariant extensions of Dirac measures on compactly cancellative topological semigroups. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 4, 699--708. doi:10.36045/bbms/1195157138. https://projecteuclid.org/euclid.bbms/1195157138