Banach spaces with the -summing property

Authors:
A. Arias, T. Figiel, W. B. Johnson and G. Schechtman

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3835-3857

MSC:
Primary 46B20

DOI:
https://doi.org/10.1090/S0002-9947-1995-1303114-X

MathSciNet review:
1303114

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Abstract: A Banach space has the -summing property if the norm of every linear operator from to a Hilbert space is equal to the -summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar field: the property is self-dual and any space with the property is a finite dimensional space of maximal distance to the Hilbert space of the same dimension. In the case of real scalars only the real line and real have the -summing property. In the complex case there are more examples; e.g., all subspaces of complex and their duals.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1303114-X

Article copyright:
© Copyright 1995
American Mathematical Society