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

  • Gilles Pisier (a1)
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.

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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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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