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
| Lingua originale | English |
|---|---|
| pagine (da-a) | 113-117 |
| Numero di pagine | 5 |
| Rivista | Quaestiones Mathematicae |
| Volume | 34 |
| Stato di pubblicazione | Published - 2011 |
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All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
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Marraffa, V., & Labuschagne, C. C. A. (2011). A note on the Banach space of preregular maps. Quaestiones Mathematicae, 34, 113-117.