Journal of Number Theory, Volume (172), No (1), Year (2017-3) , Pages (178-199)

Title : ( Advanced refinements of Young and Heinz inequalities )

Authors: M. Sababheh , Mohammad Sal Moslehian ,

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Abstract

In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove that for all $0\leq \nu\leq 1$ and each $N\in\mathbb{N}$, \begin{eqnarray*} A\#_{\nu}B+\sum_{j=1}^{N}s_{j}(\nu)\left(A\#_{\alpha_j(\nu)}B+A\#_{2^{1-j}+\alpha_j(\nu)}B-2A\#_{2^{-j}+\alpha_j(\nu)}B\right)\leq A\nabla_{\nu}B, \end{eqnarray*} for the positive operators $A$ and $B$, where $s_j(\nu)$ and $\alpha_j(\nu)$ are certain functions. Moreover, some new Heinz type inequalities involving the Hilbert-Schmidt norm are established.

Keywords

Young's inequality; norm inequalities; Heinz inequality; operator mean
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@article{paperid:1060682,
author = {M. Sababheh and Sal Moslehian, Mohammad},
title = {Advanced refinements of Young and Heinz inequalities},
journal = {Journal of Number Theory},
year = {2017},
volume = {172},
number = {1},
month = {March},
issn = {0022-314X},
pages = {178--199},
numpages = {21},
keywords = {Young's inequality; norm inequalities; Heinz inequality; operator mean},
}

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%0 Journal Article
%T Advanced refinements of Young and Heinz inequalities
%A M. Sababheh
%A Sal Moslehian, Mohammad
%J Journal of Number Theory
%@ 0022-314X
%D 2017

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