Geodesic
Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
Studia Mathematica, Tome 107 (1993) no. 2, pp. 101-113

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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.
DOI : 10.4064/sm-107-2-101-113
Keywords: spectral dilation of operator-valued measure, Hilbertian operators, factorization

V. Mandrekar 1 ; P. 1

1 
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V. Mandrekar;  P. Factorization through Hilbert space and the dilation of L(X,Y)-valued measures. Studia Mathematica, Tome 107 (1993) no. 2, pp. 101-113. doi: 10.4064/sm-107-2-101-113

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