On James’ type spaces

Sersouri, Abderrazzak

doi:10.1090/S0002-9947-1988-0973175-2

On James’ type spaces
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Trans. Amer. Math. Soc. 310 (1988), 715-745 Request permission

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.

References

Steven F. Bellenot, Transfinite duals of quasireflexive Banach spaces, Trans. Amer. Math. Soc. 273 (1982), no. 2, 551–577. MR 667160, DOI 10.1090/S0002-9947-1982-0667160-2
Gilles Godefroy, Espaces de Banach: existence et unicité de certains préduaux, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, x, 87–105 (French, with English summary). MR 511815
B. Grünbaum, On some covering and intersection properties in Minkowski spaces, Pacific J. Math. 9 (1959), 487–494. MR 105653, DOI 10.2140/pjm.1959.9.487
Robert C. James, A non-reflexive Banach space isometric with its second conjugate space, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174–177. MR 44024, DOI 10.1073/pnas.37.3.174
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8

Structure theorems for some quasi-reflexive Banach spaces

M. Valdivia, On a class of Banach spaces, Studia Math. 60 (1977), no. 1, 11–13. MR 430755, DOI 10.4064/sm-60-1-11-13