Let A be a Banach algebra with the second dual A∗∗. If A has a bounded approximate identity (= BAI), then A∗∗ is unital if and only if A∗∗ has a weak∗ bounded approximate identity(= W ∗BAI). If A is Arens regular and A has a BAI, then A∗ factors on both sides. In this paper we introduce new concepts LW ∗W and RW ∗W property and we show that under certain conditions if A has LW ∗W and RW ∗W prop...

in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

 We study the notion of bounded approximate Connes-amenability for‎ ‎dual Banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎We show that bounded approximate‎ ‎Connes-amenability of dual Banach algebras forces them to be unital‎. ‎For a separable dual Banach algebra‎, ‎we prove that bounded‎ ‎approximate Connes-amenability implies sequential approximat...

Abstract We prove that for a Banach algebra A having bounded $\mathcal {Z}(A)$ -approximate identity and every $\mathbf {[IN]}$ group G with weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) . As an application, we discuss the conditions under {Z}(L^{1}_{\omega }(G,A))$ enjoys certain algebrai...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded ap...