Let V,W∞, andW be operator ideals of completely continuous, weakly ∞-compact, and weakly compact operators, respectively. We prove that V =W∞ ◦W−1. As an immediate application, the recent result by Dowling, Freeman, Lennard, Odell, Randrianantoanina, and Turett follows: the weak Grothendieck compactness principle holds only in Schur spaces.

This paper presents new fixed point results for weakly sequentially upper semicontinuous maps defined on locally convex Hausdorff topological spaces which are angelic when furnished with the weak topology. Moreover, we establish an applicable Leray-Schauder alternative (Theorem 2.12) for a certain subclass of these maps. Our alternative combines the advantages of the strong topology (i.e., the ...

Let P : E → K be an N−homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set CP = {x ∈ E : P is weakly sequentially continuous at x}. Introduction Our interest in set of points of weak sequential continuity of a polynomial arises from the following simple observations. If P is any 2−homogeneous scalar valued polynomial on E which is weakly sequentiall...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

A Banach space X is said to be an M-space if every continuous multilinear form on X is weakly sequentially continuous. We study in this paper the stability properties of the class of M-spaces. 2000 Mathematics Subject Classification. 46B20, 46B28, 46B08.