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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
James’ space
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