Connes Amenability of $l^1$-Munn Algebras

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Ali Ghaffari
Samaneh Javadi
Ebrahim Tamimi


In this paper, we study Connes amenability of $l^1$-Munn algebras. We apply this results to semigroup algebras. We show that for a weakly cancellative semigroup $S$ with finite idempotents, amenability and Connes amenability are equivalent.

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Ghaffari, A., Javadi, S., & Tamimi, E. (2022). Connes Amenability of $l^1$-Munn Algebras. Tamkang Journal of Mathematics, 53(3), 259–266.


T. D. Blackmore, Weak amenability of discrete semigroup algebras, Semigroup Forum, 55 (1997), 196–205.

M. Daws, Connes amenability of bidual and weighted semigroup algebras, Math. Scand., 99 (2006), 217-246.

J. Duncan and A. L. T. Paterson, Amenability for discrete convolution semigroup algebras, Math. Scand., 66 (1990), 141–146.

G. H. Esslamzadeh, Banach algebra structure and amenability of a class of matrix algebras with applications, J. Funct. Anal., 161 (1999), 364–383.

G. H. Esslamzadeh, Representation theory and positive functionals of involutive l1-Munn algebras, Semigroup Forum, 69 (2004), 51–62.

G. H. Esslamzadeh, Duals and topological center of a class of matrix algebras with applications, Proc. Amer. Math. Soc., 128 (2000), 3493–3503.

G. H. Esslamzadeh, B. Shojaee and A. Mahmoodi, Approximate Connes-amenability of dual Banach algebras, Bull. Belg. Math. Soc. Simon Stevin, 19 (2012), 193–213.

A. Ghaffari and S. Javadi, φ-Connes amenability of dual Banach algebras, Bull. Iran. Math. Soc., 43 (2017), 25–39.

A. Ya. Helemskii, Homological essence of amenability in th esense of A. Connes: the injectivity of the predual bimodule, Sb. Math., 68 (1991), 555–566.

J. M. Howie, An Introduction to Semigroup Theory, Academic Press, San Diego, 1976.

B. E. Johnson, Cohomology in Banach Algebras, Mem. Amer. Math. Soc., 127(1972).

B. E. Johnson, R. V. Kadison and J. Ringrose, Cohomology of operator algebras III, Bull. Soc. Math. France, 100 (1972), 73–79.

A. T. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math., 118 (1983), 161–175.

S. M. Maepa and O. T. Mewomo, On character amenability of semigroup algebras, Quaest. Math., 39 (2016), no . 3, 307–318.

O. T. Mewomo and N. B. Okela, On approximate character amenability of Banach algebra, J. Nigerian Math. Soc., 32 (2013), 303–315.

O. T. Mewomo and O. J. Ogunsola, On n-weak amenability of semigroup algebras, J. Nigerian Math. Soc., 32 (2013), 298–301.

O. T. Mewomo, Various notions of amenability in Banach algebras, Expo. Math., 29(2011), no. 3, 283–299.

W. D. Munn, On semigroup algebras, Math. Proc. Cambridge Philos. Soc., 51(1955), 1–15.

V. I. Paulsen, Completely Bounded Maps and Dilations, Pitman Res. Notes Math. Ser.,146 Longman, Harlow/New York, 1986.

W. Rudin, Functional Analysis, McGrawHill, NewYork, 1991.

V. Runde, Amenability for dual Banach algebras, Studia Math.,148(2001), 47–66.

V. Runde, Connes amenability and normal virtual diagonals for measure algebras I, J. London Math. Soc., 67 (2003), 643–656.

V. Runde, Connes amenability and normal virtual diagonals for measure algebras II, Bull. Austral. Math. Soc., 68 (2003), 325–328.

V. Runde, Dual Banach algebras: Connes amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 95 (2004), 124–144.