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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
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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  • [1] S. A. Čobanjan, Regularity of stationary processes with values in a Banach space and factorization of operator-valued functions, Sakharth. SSR Mecn. Akad. Moambe 61 (1971), 29–32 (Russian, with Georgian and English summaries). MR 0290450
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Keywords: Banach space, positive operator-valued functions, quasi square root, factorability, regularity, stationary processes
Article copyright: © Copyright 1974 American Mathematical Society