Inequalities related to the Cauchy-Schwarz inequality
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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.
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- Inequalities related to the Cauchy-Schwarz inequality
Volume 74, Issue 1 , pp 101-111
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- standard deviation
- the Samuelson inequality
- the Cauchy-Schwarz inequality
- Primary 47A50
- Secondary 47A63