Zeitschrift für Analysis und ihre Anwendungen 23 (2004), No. 2, 303--311
Copyright Heldermann Verlag 2004
Another Version of Maher's Inequality
Salah Mecheri
Dept. of Mathematics, King Saud University, College of Science, P. O. Box 2455, Riyadh 11451, Saudi Arabia
mecherisalah@hotmail.com
[Abstract-pdf]
Let $H$ be a separable infinite dimensional complex Hilbert space, and let $ L(H)$ denote the algebra of bounded linear operators on $H$ into itself. Let $ A=(A_{1},A_{2}...,A_{n})$, $B =(B_{1},B_{2}...,B_{n})$ be n-tuples of operators in $L(H)$. We define the elementary operator $\Delta _{A,B}: L(H) \mapsto L(H)$ by $\Delta _{A,B}(X)=\sum_{i=1}^{n}A_{i}XB_{i}-X.$ In this paper we minimize the map $F_{p}(X)= \left\| T -\Delta _{A,B}(X) \right\| _{p}^{p}$, where $T\in \ker\Delta _{A,B}\cap C_{p}$, and we classify its critical points.
Keywords: Orthogonality, derivation, elementary operators.
MSC: 47B47, 47A30, 47B20; 47B10
[ Fulltext-pdf (162 KB)] for subscribers only.