A variant of Jensen’s inequality of Mercer’s type for operators with applications

Some Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

“…For inequalities for functions of selfadjoint operators, see [14]- [23], [37], [39], [40], [41], [42] and the books [24], [25] and [28].…”

Some Jensen's type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces

“…For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [3] and the references therein. For other results, see [9], [4], [8] and [6]. For recent results, see [1] and [2].…”

Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces

“…For other results see [14] and [25]. We say that the functions f, g : [a, b] −→ R are synchronous (asynchronous) on the interval [a, b] if they satisfy the following condition:…”