Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    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: http://dx.doi.org/10.1017/S0305004100064902
  • Published online: 24 October 2008
Abstract
Abstract

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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×