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.

In Dwork’s memoir [3] concerning the rationality of zeta functions, an essential role is played by the p-adic analytic function det(1− tu), where u is a certain infinite matrix. This analytic function is an entire function, exactly as in the classical Fredholm theory. It was natural to pursue this analogy and extend to u the spectral theory of F. Riesz; this is just what Dwork did ([4], §2). In...

Completely continuous operators Let A be a Banach algebra with |A| % {1}, where A := {a ∈ A : |ab| = |a| |b| for all b ∈ A} is the set of all multiplicative units in A (equivalently, A = {a ∈ A : |a| |a| = 1}). Then for any Banach modules M,N over A, an A-linear map L : M → N is continuous iff supm6=0 |L(m)| |m| < ∞. Let BA(M,N) be the space of such maps. With the norm |L| := supm6=0 |L(m)| |m|...

Given a k-linear operator T from a product of C(K) spaces into a Banach space X, our main result proves the equivalence between T being completely continuous, T having an X-valued separately ω∗ − ω∗ continuous extension to the product of the biduals and T having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to T being weakly compact, and ...

In this paper we introduce intuitionistic fuzzy completely regular weakly generalized continuous mappings and some of their properties are studied.