Abstract
Let X be a completely regular Hausdorff space and C_b(X) be the space of all bounded continuous functions on X, equipped with the strict topology beta . We study some important classes of (beta ,Vert cdot Vert _E)-continuous linear operators from C_b(X) to a Banach space (E,Vert cdot Vert _E): beta -absolutely summing operators, compact operators and beta -nuclear operators. We characterize compact operators and beta -nuclear operators in terms of their representing measures. It is shown that dominated operators and beta -absolutely summing operators T:C_b(X)rightarrow E coincide and if, in particular, E has the Radon–Nikodym property, then beta -absolutely summing operators and beta -nuclear operators coincide. We generalize the classical theorems of Pietsch, Tong and Uhl concerning the relationships between absolutely summing, dominated, nuclear and compact operators on the Banach space C(X), where X is a compact Hausdorff space.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call