6533b857fe1ef96bd12b4efd
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A note on the Banach space of preregular maps
Coenraad C.a. LabuschagneValeria Marraffasubject
Discrete mathematicsBanach lattice preregular operator regular operator.Mathematics (miscellaneous)Approximation propertySettore MAT/05 - Analisi MatematicaEberlein–Šmulian theoremInfinite-dimensional vector functionInterpolation spaceFinite-rank operatorBanach manifoldC0-semigroupLp spaceMathematicsdescription
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-03-01 | Quaestiones Mathematicae |