Title : ( An operator equality involving a continuous field of operators )
Authors: Mohammad Sal Moslehian , Fuzhen Zhang ,
دانلود فایل برای اعضای دانشگاهAccess to full-text not allowed by authors
Abstract
Let A be a C∗-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (At )t∈T be a continuous field of operators in A such that the function t → At is norm continuous on T and the function t → At is integrable. Then the following equality including Bouchner integrals holds T At − T AsdP 2 dP = T |At |2dP − T At dP 2 . (0.1) This equality is related both to the notion of variance in statistics and to a characterization of inner product spaces. With this operator equality, we present some uniform norm and Schatten p-norm inequalities. © 2008 Elsevier Inc. All rights reserved.
Keywords
, Bounded linear operator; Characterization of inner product space; Hilbert space; Q, Norm; Norm inequality; Schatten p, norm; Continuous filed of operators; Bouchner integral
@article{paperid:1006976,
author = {Sal Moslehian, Mohammad and Fuzhen Zhang},
title = {An operator equality involving a continuous field of operators},
journal = {Linear Algebra and its Applications},
year = {2008},
volume = {429},
month = {September},
issn = {0024-3795},
pages = {2159--2167},
numpages = {8},
keywords = {Bounded linear operator; Characterization of inner product space; Hilbert space; Q-Norm; Norm inequality;
Schatten p-norm; Continuous filed of operators; Bouchner integral},
}
%0 Journal Article
%T An operator equality involving a continuous field of operators
%A Sal Moslehian, Mohammad
%A Fuzhen Zhang
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2008
