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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland

Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis

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A universal homogeneous Banach space of density continuum
by
Wiesław Kubiś
Mathematical Institute, Czech Academy of Sciences, Prague, Czech Republic

Assuming the continuum hypothesis, there exists a Banach space U of density 2ℵ0 which has the following properties:


    (1) Every separable Banach space embeds isometrically into U.
    (2) Every linear isometry between separable subspaces of U extends to a bijective linear isometry of U.

These properties describe U uniquely, up to a linear isometry. The space U can be viewed as a Banach space analogue of the Cech-Stone remainder of the natural numbers. On the other hand, property (2) implies that it is not linearly isometric to any C(K) space. In the talk we shall discuss some properties of the space U and related open problems.

Date received: July 1, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxg-35.