Abstract
An example is given of a nonreflexive Banach space\(\tilde X\) that is uniformly nonoctahedral (or uniformly non-l (3)1 ), in the sense that there is a λ>1 such that there is no isomorphismT ofl (3)1 into\(\tilde X\) for which
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References
A. Beck,A convexity condition in Banach spaces and the strong law of large numbers Proc. Amer. Math. Soc.13 (1962), 329–334.
A. Brunel and L. Sucheston,On B convex Banach spaces, Math. Systems Theory7 (1973).
A. Brunel and L. Sucheston,Equal signs additive sequences in Banach spaces, to appear.
W. Davis, W. B. Johnson and J. Lindenstrauss,The l 1/n problem and degrees of non-reflexivity, to appear.
Per Enflo,Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math.13 (1972), 281–288.
D. P. Giesy and R. C. James,Uniformly non-l (1) and B-convex Banach spaces, Studia Math.48 (1973), 61–69.
D. P. Giesy,On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 114–146.
D. P. Giesy,B-convexity and reflexivity, Israel J. Math.15 (1973), 430–436.
D.P. Giesy,Super-reflexivity, stability and B-convexity, Western Michigan Univ. Math. Report29 (1972).
D. P. Giesy,The completion of a B-convex normed Riesz space is reflexive, J. Functional Analysis12 (1973), 188–198.
R. C. James,Bases and reflexivity of Banach spaces, Ann. of Math.52 (1950), 518–527.
R. C. James,A non-reflexive Banach space isometric with its second conjugate space, Proc. Nat. Acad. Sci. U. S. A.37 (1951), 174–177.
R. C. James,Uniformly nonsquare Banach spaces, Ann. of Math.80 (1964), 542–550.
R. C. James,Weak compactness and reflexivity, Israel J. Math.2 (1964), 101–119.
W. B. Johnson,On finite dimensional subspaces of Banach spaces with local unconditional structure, to appear in Studia Math.
D. Milman,On some criteria for the regularity of space of the type (B), C. R. Acad. Sci. URSS20 (1938), 243–246.
P. Meyer-Nieberg,Charakterisierung einiger topologischer und ordnungstheoretischer Eigenschaften von Banachverbanden mit Hilfe disjunkter Folgen, Arch. Math.24 (1973), 640–647.
B. J. Pettis,A proof that every uniformly convex space is reflexive, Duke Math. J.5 (1939), 249–253.
J. J. Schäffer and K. Sundaresan,Reflexivity and the girth of spheres, Math. Ann.184 (1970), 163–168.
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This research was supported in part by NSF Grant GP-28578. It was presented in preliminary form at a conference at Oberwolfach, Germany, October 15–20, 1973.
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James, R.C. A nonreflexive Banach space that is uniformly nonoctahedral. Israel J. Math. 18, 145–155 (1974). https://doi.org/10.1007/BF02756869
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DOI: https://doi.org/10.1007/BF02756869