Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
Studia Mathematica, Tome 107 (1993) no. 2, pp. 101-113
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
spectral dilation of operator-valued measure, Hilbertian operators, factorization
@article{10_4064_sm_107_2_101_113,
author = {V. Mandrekar and P.},
title = {Factorization through {Hilbert} space and the dilation of {L(X,Y)-valued} measures},
journal = {Studia Mathematica},
pages = {101--113},
year = {1993},
volume = {107},
number = {2},
doi = {10.4064/sm-107-2-101-113},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-101-113/}
}
TY - JOUR AU - V. Mandrekar AU - P. TI - Factorization through Hilbert space and the dilation of L(X,Y)-valued measures JO - Studia Mathematica PY - 1993 SP - 101 EP - 113 VL - 107 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-101-113/ DO - 10.4064/sm-107-2-101-113 LA - en ID - 10_4064_sm_107_2_101_113 ER -
%0 Journal Article %A V. Mandrekar %A P. %T Factorization through Hilbert space and the dilation of L(X,Y)-valued measures %J Studia Mathematica %D 1993 %P 101-113 %V 107 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-107-2-101-113/ %R 10.4064/sm-107-2-101-113 %G en %F 10_4064_sm_107_2_101_113
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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