## Abstract

We show that if

*E*is an atomic Banach lattice with an ordercontinuous norm,*A, B ∈ L*and^{r}(E)*M*is the operator on_{A},_{B}*L*defined by^{r}(E)*M*=_{A},_{B}(T)*AT B*then ||*M*_{A}*,*_{B}||*r =*||*A*||_{r}_{|}_{|}*B*||_{r}but that there is no real α > 0 such that ||*MA,B*|| ≥*α*||*A*||*r*||*B*||*r.*Original language | English |
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Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Early online date | 22 May 2015 |

DOIs | |

Publication status | Published - 2015 |

## Keywords

- Regular operators, basic elementary operators, Banach lattices

## ASJC Scopus subject areas

- Mathematics(all)