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Borodulin-Nadzieja, Piotr; Plebanek, Grzegorz

On sequential properties of Banach spaces, spaces of measures and densities. (English) Zbl 1224.46031

Czech. Math. J. 60, No. 2, 381-399 (2010).
Summary: We show that a conjunction of Mazur and Gelfand-Phillips properties of a Banach space \(E\) can be naturally expressed in terms of weak* continuity of seminorms on the unit ball of \(E^{*}\). 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 weak* sequential closure of atomic measures, and the set-theoretic properties of generalized densities on the natural numbers.

Cited in 6 Documents

MSC:

46B26 Nonseparable Banach spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
46E27 Spaces of measures

Keywords:

Gelfand-Phillips property; Mazur property; generalized density
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\textit{P. Borodulin-Nadzieja} and \textit{G. Plebanek}, Czech. Math. J. 60, No. 2, 381--399 (2010; Zbl 1224.46031)
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