Bulletin of the Belgian Mathematical Society - Simon Stevin

Inner invariant means on locally compact topological semigroups

B. Mohammadzadeh and R. Nasr-Isfahani

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Abstract

Let ${\cal S}$ be a locally compact semigroup and $M_a({\cal S})$ be its semigroup algebra. In this paper, we investigate inner invariant means on $L^\infty({\cal S},M_a({\cal S}))$ of all $M_a( {\cal S})$-measurable complex-valued bounded functions on ${\cal S}$ and its closed subspace $C_b({\cal S})$, the space of all bounded continuous complex-valued functions on ${\cal S}$. We also study topological inner invariant means on certain closed subspaces $X$ of $L^\infty({\cal S},M_a({\cal S}))$ and their relation with inner invariant means on $X$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 1 (2009), 129-144.

Dates
First available in Project Euclid: 25 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1235574197

Digital Object Identifier
doi:10.36045/bbms/1235574197

Mathematical Reviews number (MathSciNet)
MR2498964

Zentralblatt MATH identifier
1214.43001

Subjects
Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 43A10: Measure algebras on groups, semigroups, etc. 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc.

Keywords
Inner invariant mean locally compact semigroup topological inner invariant means

Citation

Mohammadzadeh, B.; Nasr-Isfahani, R. Inner invariant means on locally compact topological semigroups. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 129--144. doi:10.36045/bbms/1235574197. https://projecteuclid.org/euclid.bbms/1235574197


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