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november 2015 A note on the norm of a basic elementary operator
Mohamed Boumazgour, Mohamed Barraa
Bull. Belg. Math. Soc. Simon Stevin 22(4): 603-610 (november 2015). DOI: 10.36045/bbms/1447856062

Abstract

Let ${\cal L}(E)$ be the algebra of all bounded linear operators on a Banach space $E$. For $A,B\in{\cal L}(E)$, define the basic elementary operator $M_{A,B}$ by $M_{A,B}(X)=AXB$, ($X\in{\cal L}(E)$). If $\cal S$ is a symmetric norm ideal of ${\cal L}(E)$, we denote $M_{{\cal S},A,B}$ the restriction of $M_{A,B}$ to $\cal S$. In this paper, the norm equality $\|I+M_{{\cal S},A,B}\|=1+\|A\|\|B\|$ is studied. In particular, we give necessary and sufficient conditions on $A$ and $B$ for this equality to hold in the special case when $E$ is a Hilbert space and $\cal S$ is a Schatten $p$-ideal of ${\cal L}(E)$.

Citation

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Mohamed Boumazgour. Mohamed Barraa. "A note on the norm of a basic elementary operator." Bull. Belg. Math. Soc. Simon Stevin 22 (4) 603 - 610, november 2015. https://doi.org/10.36045/bbms/1447856062

Information

Published: november 2015
First available in Project Euclid: 18 November 2015

zbMATH: 1348.47028
MathSciNet: MR3429174
Digital Object Identifier: 10.36045/bbms/1447856062

Subjects:
Primary: 47A12, 47A30, 47B47

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 4 • november 2015
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