This paper is deals with the concept of weakly (Λ, sp)-continuous multifunctions. In particular, some characterizations multifunctions are investigated.

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 ...

The goal of the following is to use (infinitedimensional) linear systems theory to approach the H∞functional calculus. This extends recent work by the authors using the notion of admissible observation operators to define f (A) where f is bounded, analytic in the left half-plane and A generates an exponentially stable strongly continuous semigroup. Among other things it is shown that f (A) is a...