This article is cited in 3 papers

On Continuous Restrictions of Measurable Multilinear Mappings

E. V. Yurova

Lomonosov Moscow State University

Abstract: This article deals with measurable multilinear mappings on Fréchet spaces and analogs of two properties which are equivalent for a measurable (with respect to gaussian measure) linear functional: (i) there exists a sequence of continuous linear functions converging to the functional almost everywhere; (ii) there exists a compactly embedded Banach space $X$ of full measure such that the functional is continuous on it. We show that these properties for multilinear functions defined on a power of the space $X$ are not equivalent; but property (ii) is equivalent to the apparently stronger condition that the compactly embedded subspace is a power of the subspace embedded in $X$.

Keywords: measurable multilinear form, measurable bilinear form, Gaussian measure, compact embedding, Banach space, Radon probability measure.

UDC: 519.2

Received: 27.06.2015

DOI: 10.4213/mzm10977

 English version: Mathematical Notes, 2015, 98:6, 977–981

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