Pseudo-amenability of some weighted semigroup algebras

Subject Areas : Statistics

kobra oustad ¹ , Amin Mahmoodi ² , Mohammad Sadegh Asagri ³

1 - Department of Mathematics, Dehdasht Branch, Islamic Azad University,Dehdasht, Iran
2 - Department of Mathematics.Central Tehran Branch, Islamic Azad University,, Tehran, Iran
3 - Department of Mathematics.Central Tehran Branch, Islamic Azad University,, Tehran, Iran

Received: 2021-12-03 Accepted : 2022-05-23 Published : 2024-08-13

Keywords: نیم گروه تعویض پذیر به طور ضعیف حذفی, نیم گروه ارشمیدسی, دوتصویری,

Abstract :

We shall find some equivalence conditions for amenability/ pseudo-amenability of 〖l^1 (S,ω)〗^(**) whereas S is an inverse semigroup and ω is a weight on S. We will see that amenability, pseudo-amenability and approximate amenability of l^1 (S,ω) are the some notions for inverse semigroup S. Amenability/ pseudo-amenability of l^1 (S,ω) is characterized for some types of semigroups such as Archimedean semigroups, rectangular band semigroups and left (right) zero semigroups. We will find the relation between amenability of l^1 (S,ω) and that of 〖l^1 (S,ω)〗^(**) whenever S is an abelian weakly cancellative semigroup. Some results regording biflatness of l^1 (S,ω) for some semigroups are also included. If S be an inverse semigroup and finite and l^1 〖(S,ω)〗^(**) is pseudo-amenable, then we show that l^1 (S,ω) is biflat. Also, we will see that for a left (right) zero semigroup, l^1 (S,ω) is biflat. If 〖 S= M〗^0 (G,I) be a Brandet semigroup and l^1 (S,ω) has a bounded approximate identity, then the biflatness of 〖l^1 (S,ω)〗^(**) and the finiteness of G are equivalent.

References:

] Y. Choi, F. Ghahramani and Y. Zhang, Approximate and pseudo-amenability of various classes of Banach algebras,J.Func. Anal. 3191-3158، (2009)256.

[2] J . Duncan and I. Namioka, Amenability of inverse semigroup and their semigroup algebras, Proc. Royal- Soc . Edinburgh , Section A 321-309، (1978).

[3] M. Essmaili and A. Medghalchi , Biflatnese of certain semigroup algebras , Bulletin of the Iranian Mathematical society Vol . 39 No . 5(2013) , pp 969-959.

[4] M. Essmaili , M. Rostami , and A. R . Medghalchi, Pseudo-contractibility and Pseudo-amenability of semigroup algebrs, Arch . Math. 97 (2011) ,167 177 -.

[5] M . Essmaili ,M . Rostami, A. Pourabbas , Pseudo-amenability of certain semigroup algebras, Semigroup Forum 82 (2011) , 478-484..

[6 ] F. Ghahramani and Y. Zhang, Pseudo-amenability and pseudo-contractible Banach algebras , Math . Proc . Combridge philos . soc .142 (2007) , 111-123.

[7] A. Ya. Helemskii,Flat Banach modules and amenable algebras, Trans. Moscow Math. Soc. 47(1985), 199-224.

[8] B. E. Johnson, Approximate digonals and cohomology of certain annihilator Banach alebras, Amer. J.Math. 94 (1972), 685-698.
[9] B. E. Johnson, Cohomology in Banach algebras, Mem . Amer. Math. Soc. 127 (1972).

[10] W .D . Munn , A class of irrecucible matrix representations of an arbitrary inverse semigroup , Proc . Glasgow , math. Assoc . 5 (1961) , 41-48 .

[11] S. Naseri, Approximate amenability of weighted group algebras, International mathematical forum , vol , 6 , 2011 , no . 2 , 49-56.

[12] P. Ramsden , Biflatness of semigroup algebras , Semigroup Forum 79 (2009) , 515-530.
[13] M . Rostami , A. Pourabbas , M. Essmaili , Approximate amenability of certain inverse semigroup algebras, Acta Mathematica Scientia 2013, 33B (2) :565-577.

[14] M. Soroushmehr .M. Rostami. M. Essmaili, On pseudo-amenability of commutative semigroup algebras and their second duals,semigroup Forum, Springer Science+Business Media, LLC 2017.

[15] M. Soroushmehr, Weighted Ress matrix semigroup and their applications , Arch , Math , 100 (2013) 139-147.