Some remarks on stronger versions of the Boundary Problem for Banach spaces

Jan-David Hardtke

Ayuda

Some remarks on stronger versions of the Boundary Problem for Banach spaces

Hardtke, Jan-David ^[1]
1. [1] Freie Universität Berlin
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 1, 2011, págs. 67-80
Idioma: inglés
DOI: 10.4995/agt.2011.1702
Enlaces
- Texto completo
Resumen
- Let X be a real Banach space. A subset B of the dual unit sphere of X is said to be a boundary for X, if every element of X attains its norm on some functional in B. The well-known Boundary Problem originally posed by Godefroy asks whether a bounded subset of X which is compact in the topology of pointwise convergence on B is already weakly compact. This problem was recently solved by Pfitzner in the positive. In this note we collect some stronger versions of the solution to the Boundary Problem, most of which are restricted to special types of Banach spaces. We shall use the results and techniques of Pfitzner, Cascales et al., Moors and others.
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