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Proceedings of the American Mathematical Society

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Factorization along nest algebras


Author: Avraham Feintuch
Journal: Proc. Amer. Math. Soc. 84 (1982), 192-194
MSC: Primary 47A68; Secondary 47B35
DOI: https://doi.org/10.1090/S0002-9939-1982-0637167-5
MathSciNet review: 637167
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Abstract: Let $T$ be a positive definite operator on $\mathcal {H}$ and $\mathcal {R}$ a nest algebra in $B(\mathcal {H})$. A necessary and sufficient condition is given for the existence of a factorization for $T$ of the form $T = {A^* }A$ with $A$, ${A^{ - 1}} \in \mathcal {R}$.


References [Enhancements On Off] (What's this?)

  • William Arveson, Interpolation problems in nest algebras, J. Functional Analysis 20 (1975), no. 3, 208–233. MR 0383098, DOI https://doi.org/10.1016/0022-1236%2875%2990041-5
  • I. C. Gohberg and M. G. Kreĭn, Theory and applications of Volterra operators in Hilbert space, Translations of Mathematical Monographs, Vol. 24, American Mathematical Society, Providence, R.I., 1970. Translated from the Russian by A. Feinstein. MR 0264447
  • T. Kailath, Lectures on linear least-square estimation, Springer-Verlag, New York, 1976. D. Larson (preprint).

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Article copyright: © Copyright 1982 American Mathematical Society