Some Variants of Anderson's Inequality in $C

Volume 4, Issue 1, 2003

Article 24

SOME VARIANTS OF ANDERSON'S INEQUALITY IN C₁-CLASSES

KING SAUD UNIVERSITY COLLEGE OF SCIENCE
DEPARTMENT OF MATHEMATICS
P.O.BOX 2455, RIYADH 11451
SAUDI ARABIA.
E-Mail: mecherisalah@hotmail.com
E-Mail: bounkhel@ksu.edu.sa

Received 15 October, 2002; Accepted 19 February, 2003.
Communicated by: A.G. Babenko

ABSTRACT. The main purpose of this note is to characterize the operators $S\in \ker \Delta _{A,B}\cap C_{1}$ which are orthogonal to the range of elementary operators, where

is not a smooth point in $C_{1}$ by using the $\varphi -$ directional derivative.

Key words:
Elementary operators, Schatten p-classes, Orthogonality.

2000 Mathematics Subject Classification:
Primary 47B47, 47A30, 47B20; Secondary 47B10.

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