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Banach ideals of operators with applications to the finite dimensional structure of Banach spaces

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Abstract

We present a few applications of the theory of Banach ideals of operators. In particular, we give operator characterizations of the ℒ p spaces, compute the relative projection constant of isometric embeddings of Hilbert spaces inL p -spaces, and show that Π1 (E, F), the space of absolutely summing operators, is reflexive ifE andF are reflexive andE has the approximation property.

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Authors and Affiliations

  1. Louisiana State University, Baton Rouge, Louisiana

    Y. Gordon, D. R. Lewis & J. R. Retherford

  2. University of Florida, Gainesville, Florida

    Y. Gordon, D. R. Lewis & J. R. Retherford

Authors
  1. Y. Gordon
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  2. D. R. Lewis
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  3. J. R. Retherford
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Additional information

Research supported by NSF-GP-34193

Research supported by NSF-Science Development Grant

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Gordon, Y., Lewis, D.R. & Retherford, J.R. Banach ideals of operators with applications to the finite dimensional structure of Banach spaces. Israel J. Math. 13, 348–360 (1972). https://doi.org/10.1007/BF02762810

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  • DOI: https://doi.org/10.1007/BF02762810

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