Inequalities for quadratic polynomials in Hermitian and dissipative operators |
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Authors: | B Bollobás J.R Partington |
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Affiliation: | Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England |
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Abstract: | Let T be a Hermitian operator on a Banach space and let P be a real quadratic polynomial. Among other inequalities we give lower bounds for |P(T)x| in terms of |x|, |Tx|, and |T2x|. As a special case we deduce extensions of some classical inequalities involving derivatives of a function and obtain some new inequalities of this kind. |
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