For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

Let E be a real q-uniformly smooth Banach space whose duality map is weakly sequentially continuous. Let T : E → E be a nonexpansive mapping with F (T ) 6= ∅. Let A : E → E be an η-strongly accretive map which is also κ-Lipschitzian. Let f : E → E be a contraction map with coefficient 0 < α < 1. Let a sequence {yn} be defined iteratively by y0 ∈ E, yn+1 = αnγf(yn) + (I − αnμA)Tyn, n ≥ 0, where ...

In this paper a new class of sets called αδ-closed set is introduced and its properties are studied. Further the notion of Tαδ –Space and αδ–continuity, Super-αδ-continuity, αδirresoluteness, Strongly-αδ-super-irresoluteness are introduced. Further, we obtain some characterizations and some properties.

Objectives: The goal of this paper is to introduce the ideas Contra soft generalized** (briefly g**). Continuous functions and almost g**) – in topological spaces. Additionally, we discussed some its characteristics. Methods: To obtain definition contra g**- continuous functions, used previously introduced definition(1) (i.e. inverse image every closed set FQ g**-closed FP). Also, regular open ...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

It is shown that the tensor product JH⊗̃ǫJH fails Pe lczńyski’s property (u). The proof uses a result of Kwapień and Pe lczńyski on the main triangle projection in matrix spaces. The Banach space JH constructed by Hagler [1] has a number of interesting properties. For instance, it is known that JH contains no isomorph of l, and has property (S): every normalized weakly null sequence has a subseq...

The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...