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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. Cobanjan, Regularity of stationary processes with values in a Banach space and factorization of operator-valued functions, Sakharth. SSR Mech. Akad. Moambe 61 (1971), 29-32. (Russian) MR 44 #7631. MR 0290450 (44:7631)
  • [2] R. G. Douglas, On factoring positive operator functions, J. Math. Mech. 16 (1966), 119-126. MR 35 #782. MR 0209887 (35:782)
  • [3] H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 30 #1409. MR 0171178 (30:1409)
  • [4] A. G. Miamee and H. Salehi, Factorization of positive operator valued functions on a Banach space, Indiana Univ. Math. J. (to appear). MR 0350478 (50:2970)
  • [5] R. Payen, Fonctions aléatoires du second ordre à valeurs dans un espace de Hilbert, Ann. Inst. H. Poincaré Sect. B 3 (1967), 323-396. MR 37 #6993. MR 0231438 (37:6993)
  • [6] Ju. A. Rozanov, Some approximation problems in the theory of stationary processes, J. Multivariate Anal. 2 (1972), 135-144. MR 46 #4597. MR 0305467 (46:4597)

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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

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