Acta mathematica scientia, Series B >
APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS
Received date: 2011-10-14
Revised date: 2012-05-13
Online published: 2013-03-20
In this article, the approximate amenability of semigroup algebra ?1(S) is in-vestigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of ?1(S) are equivalent. We use this to give a direct proof of the approximate amenability of ?1(S) for a Brandt semigroup S. More-over, we characterize the approximate amenability of ?1(S), where S is a uniformly locally finite band semigroup.
Mehdi ROSTAMI , Abdolrasoul POURABBAS , Morteza ESSMAILI . APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 565 -577 . DOI: 10.1016/S0252-9602(13)60020-X
[1] Amini M, Medghalchi A R. Restricted algebras on inverse semigroups I, representation theory. Mathematische Nachrichten, 2006, 279(16): 1739–1784
[2] Bharucha P, Loy R J. Approximate and weak amenability of certain Banach algebras. Studia Math, 2010,197 (2): 195–204
[3] Choi Y. Biflatness of ?1-semilattice algebras. Semigroup Forum, 2007, 75: 253–271
[4] Choi Y, Ghahramani F. Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. Q J Math, 2011, 62(1): 39–58
[5] Choi Y, Ghahramani F, Zhang Y. Approximate and pseudo-amenability of various classes of Banach algebras. J Func Anal, 2009, 256: 3158–3191
[6] Dales H G, Lau A T, Strauss D. Banach algebras on semigroups and on their compactifications. Memoirs American Math Soc, 2010, 205: 1–165
[7] Dales H G, Loy R J. Approximate amenability of semigroup algebras and Segal algebras. Dissertationes Math (Rozprawy Mat), 2010, 474: 58
[8] Dales H G, Loy R J, Zhang Y. Approximate amenability for Banach sequence algebras. Studia Math, 2005, 177: 81–96
[9] Duncan J, Namioka I. Amenability of inverse semigroups and their semigroup algebras. Proc Roy Soc Edinburgh Sect A, 1978, 80: 309–321
[10] Duncan J, Paterson A L T. Amenability for discrete convolution semigroup algebras. Math Scand, 1990, 66 : 141–146
[11] EssmailiM, Rostami M, Pourabbas A. Pseudo-amenability of certain semigroup algebars. Semigroup Forum, 2011, 82: 478–484
[12] Ghahramani F, Loy R J. Generalized notions of amenability. J Func Anal, 2004, 208: 229–260
[13] Ghahramani F, Loy R J, Zhang Y. Generalized notions of amenability II. J Funct Anal, 2008, 254(7): 1776–1810
[14] Ghahramani F, Read C J. Approximate identities in approximate amenability. J Func Anal, 2012, 262: 3929–3945
[15] Ghahramani F, Stokke R. Approximate and pseudo-amenability of the Fourier algebra. Indiana Univ Math J, 2007, 56(2): 909–930
[16] Ghahramani F, Zhang Y. Pseudo-amenable and pseudo-contractible Banach algebras. Math Proc Cambridge Philos Soc, 2007, 142: 111–123
[17] Gheorghe F, Zhang Y. A note on approximate amenability of semigroup algebras. Semigroup Forum, 2009, 79: 349–354
[18] Howie J. Fundamental of semigroup theory. London Math Society Monographs. Volume 12. Oxford: Clarendon Press, 1995
[19] Lashkarizadeh Bami M, Samea H. Approximate amenability of certain semigroup algebras. Semigroup Forum, 2005, 71: 312–322
[20] Mehran M, Amini M. Amenability of restricted semigroup algebras. Int Journal of Math Analysis, 2010, 4(1): 17–28
[21] Paterson A L T. Amenability. Providence, RI: American Mathematical Society, 1988
[22] Ramsden P. Biflatness of semigroup algebras. Semigroup Forum, 2009, 79: 515–530
[23] Sadr M M, Pourabbas A. Approximate amenability of Banach category algebras with application to semigroup algebras. Semigroup Forum, 2009, 79: 55–64
[24] Steinberg B. M¨obius functions and semigroup representation theory. J Comb Theory, Ser A, 2006, 113(5): 866–881
[25] Steinberg B. M¨obius functions and semigroup representation theory II: character formulas and multiplicities. Advances in Math, 2008, 217: 1521–1557
/
| 〈 |
|
〉 |