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Ellipsoids defined by Banach ideal norms

Part of:Normed linear spaces and Banach spaces; Banach latticesGeneral convexity

Published online by Cambridge University Press:  26 February 2010

D. R. Lewis
D. R. Lewis
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.
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Abstract

A generalization and simplification of F. John's theorem on ellipsoids of minimum volume is proven. An application shows that for 1 ≤ p < 2, there is a subspace E of Lp and a λ > 1 such that 1E has no λ-unconditional decomposition in terms of rank one operators.

MSC classification

Secondary:46B99: None of the above, but in this section52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979, pp. 18 - 29
Copyright
Copyright © University College London 1979

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