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Isometric Characterizations of ℓnp Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
The paper establishes some characterizations of spaces in terms of p-summing or p-nuclear norms of the identity operator on the given space E.
In particular, for an n-dimensional Banach space E and I ≤ p < 2, E is isometric to if and only if πp(E*) ≥ n1/p and E* has cotype p' with the constant one.
Furthermore, spaces are characterized by inequalities for p-summing norms of operators related to the John's ellipsoid of maximal volume contained in the unit ball of E.
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- Copyright © Canadian Mathematical Society 1994