سی و نهمین کنفرانس ریاضی ایران , 2008-08-24

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.