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Necessary and sufficient conditions for factorability of nonnegative operator-valued functions on Banach space


Authors: A. G. Miamee and H. Salehi
Journal: Proc. Amer. Math. Soc. 46 (1974), 43-50
MSC: Primary 60G10; Secondary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1974-0348830-3
MathSciNet review: 0348830
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Abstract: Several necessary and sufficient conditions for factorability of positive operator-valued functions on a Banach space are given. These characterizations involve the analysis of quasi square root and their corresponding invariant subspaces. The work extends to the Banach space a recent theorem of Yu. A. Rozanov and a certain earlier result of R. Payen. It also reveals the connection between their works on the factorization problem.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0348830-3
Keywords: Banach space, positive operator-valued functions, quasi square root, factorability, regularity, stationary processes
Article copyright: © Copyright 1974 American Mathematical Society