Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
Copyright policy )Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
This paper features strong and weak compactness in spaces of vector measures with relatively compact ranges in Banach spaces. Its tools are the measure-operator identification of [16] and [24] and the description of strong and weak compactness in spaces of compact operators in [10], [11], and [29].Given a Banach space X and an algebra of sets, it is shown in [16] that under the usual identification via integration of X-valued bounded additive measures on with X-valued sup norm continuous linear operators on the space of -simple scalar functions, the strongly bounded, countably additive measures correspond exactly to those operators which are continuous for the coarser (locally convex) universal measure topology τ on . It is through the latter identification that the results on strong and weak compactness in [10], [11], and [29] can be applied to X-valued continuous linear operators on the generalized DF space to yield results on strong and weak compactness in spaces of vector measures.
- University of North Carolina at Chapel Hill United States
- University of Duisburg-Essen Germany
Derivatives of functions in infinite-dimensional spaces, universal measure topology, space of all unconditionally convergent series, measures, operators, representations of the duals of various spaces of X-valued, Radon-Nikodym property, gDF-topology, measure-operator identification, extreme points of the unit ball of the dual of a space of compact operators, Convex sets and cones of operators, Pettis- integrable functions, strong and weak compactness in spaces of measures, extreme points of the unit ball of the dual of a space of compact, representations of the duals of various spaces of X-valued measures, Spaces of measures, Compactness in topological linear spaces; angelic spaces, etc.
Derivatives of functions in infinite-dimensional spaces, universal measure topology, space of all unconditionally convergent series, measures, operators, representations of the duals of various spaces of X-valued, Radon-Nikodym property, gDF-topology, measure-operator identification, extreme points of the unit ball of the dual of a space of compact operators, Convex sets and cones of operators, Pettis- integrable functions, strong and weak compactness in spaces of measures, extreme points of the unit ball of the dual of a space of compact, representations of the duals of various spaces of X-valued measures, Spaces of measures, Compactness in topological linear spaces; angelic spaces, etc.
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