### Abstract

The aim of this paper is to give simple proofs for Jeurnink's characterizations of preregular maps in terms of Θ-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space Lβ(E, F) of all those linear maps T: E → F for which there exists a constant K such that {double pipe}Vn i=1 {pipe}Txi{pipe} ≤ K {double pipe}Vn i=1{pipe}xi for all finite sequences x1, ..., xn e{open}E. We show that, if Lβ(E; F), and the spaces L Θ (E; F) of Θ -map and Lpr(E; F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach spaces

Original language | English |
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Pages (from-to) | 113-117 |

Number of pages | 5 |

Journal | Quaestiones Mathematicae |

Volume | 34 |

Publication status | Published - 2011 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

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## Cite this

Marraffa, V., & Labuschagne, C. C. A. (2011). A note on the Banach space of preregular maps.

*Quaestiones Mathematicae*,*34*, 113-117.