Title

Inequalities for quadratic polynomials in Hermitian and dissipative operators

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. © 1984.

Publication Title

Advances in Mathematics

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