Note on the curvature and index of an almost unitary contraction operator (Q1881589)
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scientific article
| Language | Label | Description | Also known as |
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| English | Note on the curvature and index of an almost unitary contraction operator |
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Note on the curvature and index of an almost unitary contraction operator (English)
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5 October 2004
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The notions of \(d\)-contraction (``pure'' \(d\)-contraction) \(T=(T_1, \dots, T_d)\) and its curvature \(K(T)\) was introduced by \textit{W. Arveson} [Proc. Natl. Acad. Sci. USA 96, No.~20, 11096--11099 (1999; Zbl 0968.46035)]). \textit{S.~Parrott} [http://arxiv.org/abs/math.OA/0006224] proved that \(K(T)=-\text{ index}(T)\) for a single pure contraction. The aim of this note is to consider the ``non-pure'' case.
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index
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contraction operator
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curvature
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