Positivity and strict contractivity of functions of operators |
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| Authors: | Leonid Gurvits Leiba Rodman |
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| Institution: | (1) NEC Research Institute, 4 Independence Way, 08540 Princeton, NJ;(2) DIMACS, Rutgers University, 08903 New Brunswick, NJ;(3) Department of Mathematics, The College of William and Mary, 23187-8795 Williamsburg, VA |
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| Abstract: | Carathéodory class functionsf(z) are described having the property that the self-adjoint part off(A) is positive definite for every contractionA whose spectral radius is less than 1. Analogous results are obtained for bounded analytic functions in the unit disc, and for the Nevanlinna class. Applications to Markov chains are indicated.Partially supported by the US Air Force Grant AFOSR-94-0293.Partially supported by the NSF Grant DMS-9500924. |
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| Keywords: | 47A60 15A99 60J20 |
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