, Volume 74, Issue 1, pp 101-111
Date: 17 Nov 2012

Inequalities related to the Cauchy-Schwarz inequality

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Abstract

We obtain an inequality complementary to the Cauchy-Schwarz inequality in Hilbert space. The inequalities involving first three powers of a self-adjoint operator are derived. The inequalities include the bounds for the third central moment, as a special case. It is shown that an upper bound for the spectral radius of a matrix is a root of a particular cubic equation, provided all eigenvalues are positive.