Geodesic
On sequential properties of Banach spaces, spaces of measures and densities
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 381-399

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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.
Classification : 46B26, 46E15, 46E27
Keywords: Gelfand-Phillips property; Mazur property; generalized density 
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     title = {On sequential properties of {Banach} spaces, spaces of measures and densities},
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Borodulin-Nadzieja, Piotr; Plebanek, Grzegorz. On sequential properties of Banach spaces, spaces of measures and densities. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 381-399. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a6/