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Keywords:
Gelfand-Phillips property; Mazur property; generalized density
Gelfand-Phillips property; Mazur property; generalized density
Summary:
We show that a conjunction of Mazur and Gelfand-Phillips properties of a Banach space $E$ can be naturally expressed in terms of {\it weak}* continuity of seminorms on the unit ball of $E^*$. \endgraf We attempt to carry out a construction of a Banach space of the form $C(K)$ which has the Mazur property but does not have the Gelfand-Phillips property. For this purpose we analyze the compact spaces on which all regular measures lie in the {\it weak}* sequential closure of atomic measures, and the set-theoretic properties of generalized densities on the natural numbers.
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