Inequalities related to the Cauchy-Schwarz inequality
نویسندگان
چکیده
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. AMS (2000) subject classification. Primary 47A50, 15A42, 60E15; Secondary 47A63, 26D15.
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