We show that if X is a L∞-space with the Dieudonnè property and Y is a Banach space not containing l1, then any operator T : X⊗ Y → Z, where Z is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained. Let X be a L∞-space (see [1] for this notion and some useful results on L∞-spaces) and Y be a Banach space not containing l1.We consider ...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

A Banach space W with a Schauder basis is said to be α-minimal for some α < ω1 if, for any two block subspaces Z,Y ⊆ W, the Bourgain embeddability index of Z into Y is at least α. We prove a dichotomy that characterises when a Banach space has an αminimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characte...

The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin’s Maximum MM axiom), that every Asplund space of density character ω1 has a renorming with the Mazur intersection property. Combined with the previous result of Jiménez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP renormability ...

A mapping α from a normed space X into itself is called a Banach operator if there is a constant k such that 0≤ k < 1 and ‖α2(x)−α(x)‖ ≤ k‖α(x)−x‖ for all x ∈X. In this note we study some properties of Banach operators. Among other results we show that if α is a linear Banach operator on a normed space X, then N(α−1) = N((α−1)2), N(α−1)∩R(α−1)= (0) and if X is finite dimensional then X =N(α−1)⊕...

In this paper, we establish some fixed point theorems in connection with sequences of operators in the Banach space setting for Mann and Ishikawa iterative processes. Our results extend some of the results of Berinde, Bonsall, Nadler and Rus from complete metric space to the Banach space setting.