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

Piotr Borodulin-Nadzieja; Grzegorz Plebanek

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 381-399
  • ISSN: 0011-4642

Abstract

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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 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.

How to cite

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Borodulin-Nadzieja, Piotr, and Plebanek, Grzegorz. "On sequential properties of Banach spaces, spaces of measures and densities." Czechoslovak Mathematical Journal 60.2 (2010): 381-399. <http://eudml.org/doc/38014>.

@article{Borodulin2010,
abstract = {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.},
author = {Borodulin-Nadzieja, Piotr, Plebanek, Grzegorz},
journal = {Czechoslovak Mathematical Journal},
keywords = {Gelfand-Phillips property; Mazur property; generalized density; Gelfand-Phillips property; Mazur property; generalized density},
language = {eng},
number = {2},
pages = {381-399},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On sequential properties of Banach spaces, spaces of measures and densities},
url = {http://eudml.org/doc/38014},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Borodulin-Nadzieja, Piotr
AU - Plebanek, Grzegorz
TI - On sequential properties of Banach spaces, spaces of measures and densities
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 381
EP - 399
AB - 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.
LA - eng
KW - Gelfand-Phillips property; Mazur property; generalized density; Gelfand-Phillips property; Mazur property; generalized density
UR - http://eudml.org/doc/38014
ER -

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