Counter examples for pseudo-amenability of some semigroup algebras

Amir Sahami

Abstract


In this short note, we give some counter examples which show that [11, Proposition 3.5] is not true. As a consequence, the arguments in [11, Proposition 4.10] is not valid.

Keywords


Pseudo-amenability; inverse semigroup; semigroup algebras

Mathematics Subject Classification (2010)


46H10; 46H25

References


Amini, Massoud. "Module amenability for semigroup algebras." Semigroup Forum 69, no. 2 (2004): 243-254.

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

Bodaghi, Abasalt, and Massoud Amini. "Module character amenability of Banach algebras." Arch. Math. (Basel) 99, no. 4 (2012): 353-365.

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. Garth, Anthony To-Ming Lau, and Dona Papert Strauss. "Banach algebras on semigroups and on their compactifications." Mem. Amer. Math. Soc. 205, no. 966 (2010): vi+165 pp.

Essmaili, Morteza, Mehdi Rostami, and Alireza R. Medghalchi. "Pseudocontractibility and pseudo-amenability of semigroup algebras." Arch. Math. (Basel) 97, no. 2 (2011): 167-177.

Essmaili, Morteza, Mehdi Rostami, and Abdolrasoul Pourabbas. "Pseudoamenability of certain semigroup algebras." Semigroup Forum 82, no. 3 (2011): 478-484.

Ghahramani, Fereidoun, and Yong Zhang. "Pseudo-amenable and pseudocontractible Banach algebras." Math. Proc. Cambridge Philos. Soc. 142, no. 1 (2007): 111-123.

Ghahramani, Fereidoun, and Richard J. Loy. "Generalized notions of amenability." J. Funct. Anal. 208, no. 1 (2004): 229-260.

Ghahramani, Fereidoun, Richard J. Loy, and Yong Zhang. "Generalized notions of amenability. II." J. Funct. Anal. 254, no. 7 (2008): 1776-1810.

Ogunsola, Olufemi J., and Ifeyinwa E. Daniel. "Pseudo-amenability and pseudocontractibility of restricted semigroup algebra." Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018): 89-102.

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

Samei, Ebrahim, Nico Spronk, and Ross Stokke. "Biflatness and pseudoamenability of Segal algebras." Canad. J. Math. 62, no. 4 (2010): 845-869.

Zhang, Yong. Solved and unsolved problems in generalized notions of amenability for Banach algebras. Vol. 91 of Banach Center Publications. Warszawa: Inst. Mat. Pol. Acad. Sci., 2010.


Full Text: PDF

Download statistics: 431

Licencja Creative Commons
This article by Amir Sahami is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej