Delta-semidefinite and delta-convex quadratic forms in Banach spaces

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dc.creatorKalton, N.
dc.creatorKonyagin, S. V.
dc.creatorVesely, L.
dc.date2006-05-19
dc.date2007-08-28
dc.date.accessioned2026-07-07T08:25:58Z
dc.date.available2026-07-07T08:25:58Z
dc.descriptionA 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 $T\colon X\to X^*$ 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 ($1\le p \le\infty$) is: (a) delta-semidefinite iff $p \ge 2$; (b) delta-convex iff $p>1$. Some other related results concerning delta-convexity are proved and some open problems are stated.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0605549
dc.identifierhttp://arxiv.org/abs/math/0605549
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136795
dc.subjectFunctional Analysis
dc.subject46B99 (Primary); 52A41, 15A63 (Secondary)
dc.titleDelta-semidefinite and delta-convex quadratic forms in Banach spaces
dc.typetext

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