1. On sequential properties of Banach spaces, spaces of measures and densities
- Creator:
- Borodulin-Nadzieja , Piotr and Plebanek, Grzegorz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Gelfand-Phillips property, Mazur property, and generalized density
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public