Banach spaces with the 2-summing property

Arias, A.; Figiel, T.; Johnson, W. B.; Schechtman, G.

doi:10.1090/S0002-9947-1995-1303114-X

Banach spaces with the $2$-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 $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-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 $\ell _\infty ^2$ have the $2$-summing property. In the complex case there are more examples; e.g., all subspaces of complex $\ell _\infty ^3$ and their duals.

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