Operator Inequalities of the Jensen, Čebyšev and Grüss Type

Abstract

-1. Functions of Selfadjoint Operators in Hilbert Spaces (Introduction, Bounded Selfadjoint Operators, Continuous Functions of Selfadjoint Operators, Step Functions of Selfadjoint Operators, The Spectral Decomposition of Selfadjoint Operators, References). -2. Inequalities of the Jensen Type ( Introduction, Reverses of the Jensen Inequality, Some Slater Type Inequalities, Other Inequalities for Convex Functions, Some Jensen Type Inequalities for Twice Differentiable Functions, Some Jensen's Type Inequalities for Log-convex Functions, Hermite-Hadamard's Type Inequalities, Hermite-Hadamard's Type Inequalities for Operator Convex Functions, References). -3. Inequalities of the Cebysev and Gruss Type (Introduction, Cebysev's Inequality, Gruss Inequality, More Inequalities of Gruss Type, More Inequalities for the Cebysev Functional, Bounds for the Cebysev Functional of Lipschitzian Functions, Quasi Gruss Type Inequalities, Two Operator Gruss Type Inequalities, References).