Inequalities for quadratic polynomials in Hermitian and dissipative operators
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.
Advances in Mathematics
Bollobás, B., & Partington, J. (1984). Inequalities for quadratic polynomials in Hermitian and dissipative operators. Advances in Mathematics, 51 (3), 271-280. https://doi.org/10.1016/0001-8708(84)90012-4