Data di Pubblicazione:
2008
Citazione:
Delta-semidefinite and delta-convex quadratic forms in Banach spaces / N. Kalton, S.V. Konyagin, L. Vesely. - In: POSITIVITY. - ISSN 1385-1292. - 12:2(2008), pp. 221-240. [10.1007/s11117-007-2106-6]
Abstract:
A continuous quadratic form (“quadratic form”, in short) on a Banach space X is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if T is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional L p (μ) space (1 ≤ p ≤ ∞) is: (a) delta-semidefinite iff p ≥ 2; (b) delta-convex iff p > 1. Some other related results concerning delta-convexity are proved and some open probms are stated.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Banach space ; continuous quadratic form ; positively semidefinite quadratic form ; delta-semidefinite quadratic form ; delta-convex function ; Walsh-Paley martingale
Elenco autori:
N. Kalton, S.V. Konyagin, L. Vesely
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