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    Blanco, A. and Grønbæk, N. 2009. Amenability of algebras of approximable operators. Israel Journal of Mathematics, Vol. 171, Issue. 1, p. 127.

    Adell, J. A. and de la Cal, J. 1996. Bernstein-type operators diminish the φ-variation. Constructive Approximation, Vol. 12, Issue. 4, p. 489.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 103, Issue 2
  • March 1988, pp. 323-331

The dual J* of the James space has cotype 2 and the Gordon-Lewis property

  • Gilles Pisier (a1)
  • DOI:
  • Published online: 24 October 2008

We prove the result in the title. More generally we consider the Banach space υp, of all sequences (xn) of scalars such that

where the supremum runs over all increasing sequences n1n2 ≤ …. We show that is of cotype 2 if p ≽ 2 and of cotype p′, where 1/p′ + 1/p = 1, if p ≤ 2. Similar results are obtained for the analogous function spaces.

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[1]M. Bruneau . Variation totale d'une fonction. Lecture Notes in Math. vol. 413 (Springer-Verlag, 1974).

[3]Y. Gordon and D. Lewis . Absolutely summing operators and local unconditional structures. Acta Math. 133 (1974), 2748.

[5]R. C. James . A non reflexive Banach space isometric with its second conjugate space. Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174177.

[7]W. B. Johnson , J. Lindenstrauss and G. Schechtman . On the relation between several notions of unconditional structure. Israel J. Math. 37 (1980), 120129.

[9]S. V. Kisliakov . A remark on the space of functions of bounded p-variation. Math. Nachr. 119 (1984), 137140.

[12]A. Pietsch . Operator Ideals North-Holland, 1980).

[16]S. Reisner . On Banach spaces having the property G.L.. Pacific J. Math. 83 (1979), 505521.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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