An operator inequality and its consequences
Copyright policy )An operator inequality and its consequences
Let f be a continuous convex function on an interval J, let A, B, C, D be self-adjoint operators acting on a Hilbert space with spectra contained in J such that A+D=B+C and A<=m<=B, C<=M<=D for two real numbers m< M and let Phi be a unital positive linear map on B(H). We prove the subadditive inequality f(Phi(B))+f(Phi(C)<= Phi(f(A))+Phi(f(D)) and apply it to obtain several inequalities such as the Jensen-Mercer operator inequality and the Petrovic operator inequality.
- Ferdowsi University of Mashhad Iran (Islamic Republic of)
- University of Zagreb Croatia
convex function, operator inequalities, Petrović operator inequality, Jensen-Mercer operator inequality, functional calculus, Convexity of real functions in one variable, generalizations, Petrovi, Operator means involving linear operators, shorted linear operators, etc., operator convexity, Linear operator inequalities, convex function; positive linear map; Jensen-Mercer operator inequality; Petrovi, positive linear map, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
convex function, operator inequalities, Petrović operator inequality, Jensen-Mercer operator inequality, functional calculus, Convexity of real functions in one variable, generalizations, Petrovi, Operator means involving linear operators, shorted linear operators, etc., operator convexity, Linear operator inequalities, convex function; positive linear map; Jensen-Mercer operator inequality; Petrovi, positive linear map, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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