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Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

V. Mandrekar;  P. Richard — 1993

Studia Mathematica

We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.

The Markov property for generalized gaussian random fields

G. Kallianpur;  V. Mandrekar — 1974

Annales de l'institut Fourier

We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in R n ) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.

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