On sequential properties of Banach spaces, spaces of measures and densities

Title:

On sequential properties of Banach spaces, spaces of measures and densities

Creator:

Borodulin-Nadzieja , Piotr and Plebanek, Grzegorz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f7f3dde1-eaa5-48b7-bc2e-8d95994d23be
uuid:f7f3dde1-eaa5-48b7-bc2e-8d95994d23be

Subject:

Gelfand-Phillips property, Mazur property, and generalized density

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

381-399

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:2

Harvested from:

CDK

Metadata only:

false