MODULUS OF CONTINUITY OF OPERATOR FUNCTIONS

被引：6

作者：

Farforovskaya, Yu. B. ^{[1
]}

Nikolskaya, L. ^{[2
]}

机构：

[1] State Univ Telecommun, Dept Math, St Petersburg, Russia

[2] Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence, France

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2009年 / 20卷 / 03期

关键词：

Selfadjoint operator; operator function; modulus of continuity; INTEGRALS;

D O I：

10.1090/S1061-0022-09-01058-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A and B be bounded selfadjoint operators on a separable Hilbert space, and let f be a continuous function defined on an interval [a, b] containing the spectra of A and B. If omega(f) denotes the modulus of continuity of f, then parallel to f(A) - f(B)parallel to <= 4[log (b - a/parallel to A - B parallel to +1) + 1](2) . omega(f)(parallel to A - B parallel to). A similar result is true for unbounded selfadjoint operations, under sonic natural assumptions on the growth of f.

引用

页码：493 / 506

页数：14

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