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Points of Weak$^\ast$-Norm Continuity in the Unit Ball of the Space $\WC(K,X)^\ast$

  Published:1999-03-01
 Printed: Mar 1999
  • T. S. S. R. K. Rao
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Abstract

For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak$^\ast$-norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property.
Keywords: Points of weak$^\ast$-norm continuity, space of vector valued weakly continuous functions, $M$-ideals Points of weak$^\ast$-norm continuity, space of vector valued weakly continuous functions, $M$-ideals
MSC Classifications: 46B20, 46E40 show english descriptions Geometry and structure of normed linear spaces
Spaces of vector- and operator-valued functions
46B20 - Geometry and structure of normed linear spaces
46E40 - Spaces of vector- and operator-valued functions
 

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