Double operator integrals and their estimates in the uniform norm

被引：0
|
作者：
Farforovskaya Yu.B.
机构：
来源：
Journal of Mathematical Sciences | 1998年 / 92卷 / 1期
关键词：
Lipschitz Function; Lipschitz Constant; Nonlinear Estimate; Entire Real Line; Finite Spectrum;
D O I：
10.1007/BF02440150
中图分类号：
学科分类号：
摘要：
In this paper, conditions are considered for the existence of the double operator integral ∫∫ φ(λ,μ)dEλTdFμ, where Eλ, Fμ are the spectral functions of two self-adjoint operators A, B on a Hilbert space and T is a bounded operator. In principal, the case where A has finite spectrum is studied. Nonlinear estimates of ||f(A)T-Tf(B)|| in terms of the norm of ||AT-TB|| for f ∈ Lip 1 are deduced. Also, a formula for the Fréchet derivative is presented. Bibliography: 16 titles. © 1998 Plenum Publishing Corporation.
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页码：3640 / 3656
页数：16
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