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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 2, 2004, pp. 303–311
DOI: 10.4171/ZAA/1200

Published online: 2004-06-30

Another Version of Maher's Inequality

Salah Mecheri[1]

(1) King Saud University, Riyadh, Saudi Arabia

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

Mecheri Salah: Another Version of Maher's Inequality. Z. Anal. Anwend. 23 (2004), 303-311. doi: 10.4171/ZAA/1200