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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
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?)

  • [1] W. A. Arveson, Interpolation in nest algebras, J. Funct. Anal. 20 (1975), 208-233. MR 0383098 (52:3979)
  • [2] I. C. Gohberg and M. G. Krein, Theory and applications of Volterra operators in Hilbert space, Transl. Math. Monos., vol. 24, Amer. Math. Soc., Providence, R.I., 1970. MR 0264447 (41:9041)
  • [3] T. Kailath, Lectures on linear least-square estimation, Springer-Verlag, New York, 1976.
  • [4] D. Larson (preprint).

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Article copyright: © Copyright 1982 American Mathematical Society

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