in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between t...

In the present paper, we consider a topological space equipped with an ideal, a theme that has been treated by Vaidyanathaswamy [15] and Kuratowski [6] in their classical texts. An ideal on a set X is a nonempty subset of P(X), the power set of X , which is closed for subsets and finite unions. An ideal is also called a dual filter. {φ} and P(X) are trivial examples of ideals. Some useful ideal...

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.