Pseudo-amenability and pseudo-contractibility of restricted semigroup algebra

Olufemi Johnson Ogunsola, Ifeyinwa E. Daniel

Abstract


In this article the pseudo-amenability and pseudo-contractibility of restricted semigroup algebra lr1(S) and semigroup algebra, l1(Sr) on restricted semigroup, Sr are investigated for different classes of inverse semigroups such as Brandt semigroup, and Clifford semigroup. We particularly show the equivalence between pseudo-amenability and character amenability of restricted semigroup algebra on a Clifford semigroup and semigroup algebra on a restricted semigroup. Moreover, we show that when S=M0(G,I) is a Brandt semigroup, pseudo-amenability of l1(Sr) is equivalent to its pseudo-contractibility.

Keywords


pseudo-amenable; pseudo-contractible; restricted semigroup; semigroup algebra

Mathematics Subject Classification (2010)


Primary: 46H20; Secondary: 46H10, 46H25.

References


Arens, Richard. "The adjoint of a bilinear operation." Proc. Amer. Math. Soc. 2, (1951): 839-848.

Bodaghi, Abasalt, and Ali Jabbari. "Module pseudo-amenability of Banach algebras." An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 63, no. 3 (2017): 449-461.

Dales, H. G. Banach algebras and automatic continuity. Vol. 24 of London Mathematical Society Monographs. New Series. New York: Oxford Science Publications, The Clarendon Press, Oxford University Press, 2000.

Dales, H. G., and A.T.-M. Lau, and D. Strauss. "Banach algebras on semigroups and on their compactifications." Mem. Amer. Math. Soc. 205, no. 966 (2010): i-165.

Duncan, John, and Isaac Namioka. "Amenability of inverse semigroups and their semigroup algebras." Proc. Roy. Soc. Edinburgh Sect. A 80, no. 3-4 (1978): 309-321.

Duncan, John, and S.A.R. Hosseiniun. "The second dual of a Banach algebra." Proc. Roy. Soc. Edinburgh Sect. A 84, no. 3-4, (1979): 309-325.

Essmaili, M., and M. Rostami, and A.R. Medghalchi. "Pseudo-contractibility and pseudo-amenability of semigroup algebras." Arch. Math. (Basel) 97, no. 2 (2011): 167-177.

Essmaili, M., and M. Rostami, and A. Pourabbas. "Pseudo-amenability of certain semigroup algebras." Semigroup Forum 82, no. 3 (2011): 478-484.

Ghahramani, F., and Y. Zhang. "Pseudo-amenable and pseudo-contractible Banach algebras." Math. Proc. Cambridge Philos. Soc. 142, no. 1 (2007): 111-123.

Lawson, Mark V. Inverse semigroups. The theory of partial symmetries. River Edge, NJ: World Scientific Publishing Co., Inc., 1998.

Amini, Massoud, and Alireza Medghalchi. "Restricted algebras on inverse semigroups. I. Representation theory." Math. Nachr. 279, no. 16 (2006): 1739-1748.

Mewomo, O.T. "Notions of amenability on semigroup algebras." J. Semigroup Theory Appl. 2013 (2013): art id. 8.

Mewomo, O. T., and O.J. Ogunsola. "On character amenability of restricted semigroup algebras." Proc. Jangjeon Math. Soc. 19, no. 3 (2016): 591-607.

Mehran, Mohammad and Massoud Amini. "Amenability of restricted semigroup algebras." Int. J. Math. Anal. (Ruse) 4, no. 1-4 (2010): 17-28.

Munn, W. D. "A class of irreducible matrix representations of an arbitrary inverse semigroup." Proc. Glasgow Math. Assoc. 5 (1961): 41-48.

Ramsden, Paul. "Biflatness of semigroup algebras." Semigroup Forum 79, no. 3 (2009): 515-530.

Rostami, Mehdi, and Abdolrasoul Pourabbas, and Morteza Essmaili. "Approximate amenability of certain inverse semigroup algebras." Acta Math. Sci. Ser. B (Engl. Ed.) 33, no. 2 (2013): 565-577.

Runde, Volker. Lectures on amenability. Vol. 1774 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 2002.

Sadr, Maysam Maysami. "Pseudo-amenability of Brandt semigroup algebras." Comment. Math. Univ. Carolin. 50, no. 3 (2009): 413-419.


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