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

Miamee, A. G.; Salehi, H.

doi:10.1090/S0002-9939-1974-0348830-3

Necessary and sufficient conditions for factorability of nonnegative operator-valued functions on Banach space
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by A. G. Miamee and H. Salehi

Proc. Amer. Math. Soc. 46 (1974), 43-50

DOI: https://doi.org/10.1090/S0002-9939-1974-0348830-3

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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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