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.
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页码：287 / 303
页数：16
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