×

zbMATH — the first resource for mathematics

On James’ type spaces. (English) Zbl 0706.46021
Summary: We study the spaces E which are isometric to their biduals \(E^{**}\), and satisfy \(\dim (E^{**}/E)<\infty\). We show that these spaces have several common points with the usual James’ space.
Our study leads to a kind of classification of these spaces and we show that there are essentially four different basic structures for such spaces in the complex case, and five in the real case.

MSC:
46B25 Classical Banach spaces in the general theory
46B10 Duality and reflexivity in normed linear and Banach spaces
46B20 Geometry and structure of normed linear spaces
Keywords:
James’ space
PDF BibTeX XML Cite
Full Text: DOI