##### Title: Some Generalized Notions of Amenability Modulo an Ideal

##### Pages: 178-184

##### Cite as:

Hosein Esmaili, Hamidreza Rahimi, Some Generalized Notions of Amenability Modulo an Ideal, Int. J. Anal. Appl., 13 (2) (2017), 178-184.#### Abstract

In this paper some generalized notions of amenability modulo an ideal of Banach algebras such as uniformly (boundedly) approximately amenable (contractible) modulo an ideal of Banach algebras are investigated. Using the obtained results, uniformly (boundedly) approximately amenability (contractibility) modulo an ideal of weighted semigroup algebras are characterized.

##### Full Text: PDF

#### References

- M. Amini and H. Rahimi, Amenability of semigroups and their algebras modulo a group congruence, Acta Math. Hung., 144 (2) (2014), 407-415.
- Y. Choi and F. Ghahramani, Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras, Quart. J. Math. 62 (2011), 39-58.
- A. H. Clifford and J. B. Preston, The Algebraic Theory of Semigroups I, American Mathematical Society, Surveys 7, American Mathematical Society, Providence (1961).
- H.G. Dales. Banach algebras and automatic continuity, Clarendon Press, Oxford,(2000).
- F. Ghahramani, R. J. Loy Generalized notions of amenability, J. Funct. Anal, 208, (2004), 229-260.
- F. Ghahramani, R. J. Loy, and Y. Zhang, Generalized notions of amenability, II, J. Functional Analysis 254 (2008), 1776-1810.
- F. Ghahramani, E. Samei and Y. Zhang, Generalized amenability properties of the Beurling algebras, J. Aust. Math. Soc. 89 (2010), 359-376.
- R. S. Gigon, Congruences and group congruences on a semigroup, Semigroup Forum, 86 (2013), 431-450.
- J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford (1995).
- H. Rahimi and Kh. Nabizadeh, Amenability Modulo an Ideal of Second Duals of Semigroup Algebras, Mathematics, 4 (3) (2016), Art. ID 55.
- H. Rahimi and E. Tahmasebi, Hereditary properties of amenability modulo an ideal of Banach algebras, J. Linear Topol. Algebra, 3 (2) (2014), 107- 114.
- H. Rahimi and A. Soltani, Approximate amenability modulo an ideal of Banach algebras, U.P.B. Sci. Bull., Series A, 78 (3) (2016), 233-240.
- M. Siripitukdet and S. Sattayaporn, The least group congruence on E-inversive semigroups and E-inversive E-semigroups, Thai Journal of Mathematics, 3 (2005), 163-169.