Norms of basic elementary operators on algebras of regular operators

Wickstead, A.

doi:10.1090/proc/12664

Norms of basic elementary operators on algebras of regular operators
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by A. W. Wickstead PDF

Proc. Amer. Math. Soc. 143 (2015), 5275-5280 Request permission

Abstract:

We show that if $E$ is an atomic Banach lattice with an order continuous norm, $A,B\in \mathcal {L}^r(E)$ and $M_{A,B}$ is the operator on $\mathcal {L}^r(E)$ defined by $M_{A,B}(T)=ATB$, then $\|M_{A,B}\|_r=\|A\|_r\|B\|_r$ but that there is no real $\alpha >0$ such that $\|M_{A,B}\|\ge \alpha \|A\|_r\|B\|_r$.

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