Advanced refinements of Young and Heinz inequalities

被引：28

作者：

Sababheh, M. ^{[1
]}

Moslehian, M. S. ^{[2
]}

机构：

[1] Princess Sumaya Univ Technol, Dept Basic Sci, Amman 11941, Jordan

[2] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159, Mashhad 91775, Iran

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 172卷

关键词：

Young's inequality; Norm inequalities; Heinz inequality; OPERATOR INEQUALITIES;

D O I：

10.1016/j.jnt.2016.08.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 <= v <= 1 and each N is an element of N, A#(nu) B + [GRAPHICS] s(j)(nu) (A#B-alpha j(nu) + A#(21-j) + alpha(j)(nu)B -2A#(2-j) + alpha(j)(nu)B) <= A del B-nu, 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. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：178 / 199

页数：22

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