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A skew normal dilation on the numerical range of an operator

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Abstract.

Simple facts about the Poincaré-Neumann double layer potential are used in the construction of a normal dilation, on the numerical range of an arbitrary Hilbert space operator. Recent and old ideas in the theory of the numerical range are unified by this framework. A couple of mapping results for the numerical range are derived.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Mihai Putinar & Sebastian Sandberg

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  1. Mihai Putinar
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  2. Sebastian Sandberg
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Correspondence to Mihai Putinar.

Additional information

Revised version: 15 July 2002

First author partially supported by the National Science Foundation Grant DMS 0100367, Second author supported by STINT, The Swedish Foundation for International Cooperation in Research and Higher Education.

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Putinar, M., Sandberg, S. A skew normal dilation on the numerical range of an operator. Math. Ann. 331, 345–357 (2005). https://doi.org/10.1007/s00208-004-0585-3

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