The Giesy-James theorem for general index p, with an application to operator ideals on the pth James space

Bird, Alistair and Jameson, Graham and Laustsen, Niels (2013) The Giesy-James theorem for general index p, with an application to operator ideals on the pth James space. Journal of Operator Theory, 70 (1). pp. 291-307.

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Abstract

A theorem of Giesy and James states that c0 is finitely representable in James' quasi-reflexive Banach space J2. We extend this theorem to the pth quasi-reflexive James space Jp for each p∈(1,∞). As an application, we obtain a new closed ideal of operators on Jp, namely the closure of the set of operators that factor through the complemented subspace (l∞1⊕l∞2⊕...⊕l∞n⊕...)lp of Jp.