Pełczyński's Property (V) on spaces of vector-valued functions

Pelczyński’s Property (v) on Spaces of Vector-valued Functions

Let E be a separable Banach space and Ω be a compact Hausdorff space. It is shown that the space C(Ω, E) has property (V) if and only if E does. Similar result is also given for Bochner spaces L(μ,E) if 1 < p < ∞ and μ is a finite Borel measure on Ω.

Realcompactness and spaces of vector-valued functions

It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y, F ) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y ; in particular we find remarkable differences with respect to t...

Isometries on Spaces of Vector Valued Lipschitz Functions

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.

On Spaces of Measurable Vector - Valued Functions 399 Proof

Nuclear Operators on Spaces of Continuous Vector-Valued Functions

Abstract Let Ω be a compact Hausdorff space, let E be a Banach space, and let C(Ω, E) stand for the Banach space of all E-valued continuous functions on Ω under supnorm. In this paper we study when nuclear operators on C(Ω, E) spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if F is a Banach space and if T : C(Ω, E) → F is a ...