Hereditary properties of amenability modulo an ideal of Banach algebras

Subject Areas : Abstract harmonic analysis

H. Rahimi ¹ , E. Tahmasebi ²

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Tehran, Iran

Received: 2014-07-08 Accepted : 2014-09-22 Published : 2014-10-04

Keywords: Amenability modulo an ideal, Neo-unital modulo an ideal, Approximate identity modulo an ideal,

Abstract :

In this paper we investigate some hereditary properties of amenability modulo anideal of Banach algebras. We show that if $(e_\alpha)_\alpha$ is a bounded approximate identity modulo Iof a Banach algebra A and X is a neo-unital modulo I, then $(e_\alpha)_\alpha$is a bounded approximateidentity for X. Moreover we show that amenability modulo an ideal of a Banach algebra Acan be only considered by the neo-unital modulo I Banach algebra over A.

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