Title : ( Riemann sums for self-adjoint operators )
Authors: J. Rooin , A. Alikhani , Mohammad Sal Moslehian ,
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Abstract
This paper focuses on Riemann sums for the functional calculus of bounded self-adjoint operaors. We first obtain some monotonicity properties of operator convex functions. Using these results we then refine an operator Hermite--Hadamard type inequality. Finally we extend the Alzer and Bennet inequalities to operators on Hilbert spaces.
Keywords
, Hermite, , Hadamard inequality; operator convex function; Alzer inequality; Bennet inequality; operator inequality
@article{paperid:1041236,
author = {J. Rooin and A. Alikhani and Sal Moslehian, Mohammad},
title = {Riemann sums for self-adjoint operators},
journal = {Mathematical Inequalities and Applications},
year = {2014},
volume = {17},
number = {3},
month = {March},
issn = {1331-4343},
pages = {1115--1124},
numpages = {9},
keywords = {Hermite--Hadamard inequality; operator convex function;
Alzer inequality; Bennet inequality; operator inequality},
}
%0 Journal Article
%T Riemann sums for self-adjoint operators
%A J. Rooin
%A A. Alikhani
%A Sal Moslehian, Mohammad
%J Mathematical Inequalities and Applications
%@ 1331-4343
%D 2014
