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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On James' type spaces


Author: Abderrazzak Sersouri
Journal: Trans. Amer. Math. Soc. 310 (1988), 715-745
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9947-1988-0973175-2
MathSciNet review: 973175
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Abstract: We study the spaces $ E$ which are isometric to their biduals $ {E^{{\ast}{\ast}}}$, and satisfy $ \dim ({E^{{\ast}{\ast}}}/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.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0973175-2
Article copyright: © Copyright 1988 American Mathematical Society