(2n+1)-Weak Module Amenability of Triangular Banach Algebras on Inverse Semigroup Algebras

Document Type : Original Research Articles

Authors
Ebrahim Nasrabadi 1
Mohammad Ramezanpour 2
Asadollah Aasaraai 3
1 Department of Mathematic, Faculty of Mathematic Science and Statistic‎s, University of Birjand, Birjand, Islamic Republic of Iran
2 School of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎ Islamic Republic of Iran
3 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Islamic Republic of Iran
10.22059/jsciences.2021.295337.1007478
Abstract
Let  be a commutative (not necessary unital) inverse semigroup with the set of idempotents  ‎then  is a commutative Banach‎ -module with canonical actions‎. ‎Recently‎, ‎it is shown that the triangular Banach algebra
‎
is -weakly -module amenable‎, ‎provided that  and  is unital or  satisfies condition  for some ‎. ‎In this paper‎, ‎we show that  is -weakly -module amenable‎, ‎without any additional conditions on  and , ‎if  is a certain quotient space of .
Keywords
Inverse semigroup
Triangular Banach algebra
First module cohomology group
Weak module amenability, ("n)" -weak module amenability
  1. Forrest BE, Marcoux LW. Derivation of triangular Banach algebras. Indiana Univ Math. Soc. 1996;45: 441-62.
  2. Forrest BE, Marcoux LW. Weak amenability of triangular Banach algebras. Tranc. Amer, Math. Soc. 2002;354(4): 1435-52.
  3. Amini M, Bagha DE. Weak module amenability for semigroup algebras. Semigroup forum. 2005;71: 18-26.
  4. Bodaghi A, Amini M, Jabbari A. Permanent weak module amenability of semigroup algebras. Ann. Alexandru. Ioan. Cuza. Univ. Math. 2015;63(2): 287-96.
  5. Nasrabadi E, Pourabbas AR. Module cohomology group of inverse semigroup algebras. Bull. Irannian Math. Soc. 2011;37(4): 157-69.
  6. Bodaghi A, Jabbari A. n-Weak module amenability of triangular Banach algebras. Math. Slovaca. 2015;65(3): 645-66.
  7. Pourabbas AR, Nasrabadi E. Weak module amenability of triangular Banach algebras, Math. Slovaca. 2011;61: 949-58.
  8. Nasrabadi E. Weak module amenability of triangular Banach algebras II. Math. Slovaca. 2018;69(2): 425-32.
  9. Amini M. Module amenability for semigroup algebras. Semigroup Forum. 2004;69: 243-54.
Journal of Sciences, Islamic Republic of Iran
Volume 32, Issue 4
Autumn 2021
Pages 341-347