location:  Publications → journals → CMB
Abstract view

# 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
 Format: HTML LaTeX MathJax PDF PostScript

## 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
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 46E40 - Spaces of vector- and operator-valued functions