Title : ( AN OPERATOR EQUALITY INVOLVING A CONTINUOUS FIELD OF OPERATORS )
Authors: Mohammad Sal Moslehian , F. Zhang ,
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Abstract
Let (At)t2T be a continuous field of operators in a C-algebra A. Under certain conditions we show that ZT At − ZT AsdP 2 dP = ZT |At|2dP − ZT AtdP 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.
Keywords
, Bounded linear operator; characterization of inner product space; Hilbert space; Q-norm; norm inequality; Schatten p-norm; continuous filed of operators, Bouchner integral.
@inproceedings{paperid:1006987,
author = {Sal Moslehian, Mohammad and F. Zhang},
title = {AN OPERATOR EQUALITY INVOLVING A CONTINUOUS FIELD OF OPERATORS},
booktitle = {سی و نهمین کنفرانس ریاضی ایران},
year = {2008},
location = {کرمان, IRAN},
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 Conference Proceedings
%T AN OPERATOR EQUALITY INVOLVING A CONTINUOUS FIELD OF OPERATORS
%A Sal Moslehian, Mohammad
%A F. Zhang
%J سی و نهمین کنفرانس ریاضی ایران
%D 2008
