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.
@article{bwmeta1.element.bwnjournal-article-smv107i2p101bwm,
author = {V. Mandrekar and P. Richard},
title = {Factorization through Hilbert space and the dilation of L(X,Y)-valued measures},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {101-113},
zbl = {0812.47016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv107i2p101bwm}
}
Mandrekar, V.; Richard, P. Factorization through Hilbert space and the dilation of L(X,Y)-valued measures. Studia Mathematica, Tome 104 (1993) pp. 101-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv107i2p101bwm/
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