Some inequalities for continuous functions of selfadjoint operators in hilbert spaces

被引：4

作者：

Dragomir S.S. ^{[1
,2
]}

机构：

[1] Mathematics, School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City

[2] School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg

来源：

Acta Mathematica Vietnamica | 2014年 / 39卷 / 3期

关键词：

Functions of selfadjoint operators; Inequalities for selfadjoint operators; Selfadjoint operators; Spectral representation;

D O I：

10.1007/s40306-014-0061-4

中图分类号：

学科分类号：

摘要：

If Eλ∈R is the spectral family of a bounded selfadjoint operator A on a Hilbert space H and m=minSp(A) and M=maxSp(A), we show that for any continuous function φ: m,M] → C, we have the inequality φ (A) x,y2≤ (∈tm-0M(t) ,d (m-0t(E.x,y)))2(A)y,y for any vectors x and y from H. Some related results and applications are also given. © 2014 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

引用

页码：287 / 303

页数：16

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