Bulletin of the Belgian Mathematical Society - Simon Stevin

A note on the norm of a basic elementary operator

Mohamed Boumazgour and Mohamed Barraa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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 ${\cal L}(E)$.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 4 (2015), 603-610.

First available in Project Euclid: 18 November 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A12: Numerical range, numerical radius 47A30: Norms (inequalities, more than one norm, etc.) 47B47: Commutators, derivations, elementary operators, etc.

Norms elementary operators norm ideals numerical range


Boumazgour, Mohamed; Barraa, Mohamed. A note on the norm of a basic elementary operator. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 4, 603--610. doi:10.36045/bbms/1447856062. https://projecteuclid.org/euclid.bbms/1447856062

Export citation