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Interpolation and Factorization of Operators

Steven Bloom, Anita Tabacco Vignati and Marco Vignati
Proceedings of the American Mathematical Society
Vol. 102, No. 3 (Mar., 1988), pp. 567-576
DOI: 10.2307/2047225
Stable URL: http://www.jstor.org/stable/2047225
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Interpolation and Factorization of Operators
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Abstract

We apply the complex method of interpolation to families of infinite-dimensional, separable Hilbert spaces, and obtain a detailed description of the structure of the interpolation spaces, by means of a unique "extremal" operator-valued, analytic function. We use these interpolation techniques to give a different proof, under weaker assumptions, of a theorem of A. Devinatz concerning the factorization of positive, infinite-rank, operator-valued functions.

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