A note on the Banach space of preregular maps

Valeria Marraffa, Coenraad C. A. Labuschagne

Risultato della ricerca: Article

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 originaleEnglish
pagine (da-a)113-117
Numero di pagine5
RivistaQuaestiones Mathematicae
Volume34
Stato di pubblicazionePublished - 2011

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Banach space
Banach Lattice
L-space
Linear map
Norm

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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A note on the Banach space of preregular maps. / Marraffa, Valeria; Labuschagne, Coenraad C. A.

In: Quaestiones Mathematicae, Vol. 34, 2011, pag. 113-117.

Risultato della ricerca: Article

Marraffa, V & Labuschagne, CCA 2011, 'A note on the Banach space of preregular maps', Quaestiones Mathematicae, vol. 34, pagg. 113-117.
Marraffa, Valeria ; Labuschagne, Coenraad C. A. / A note on the Banach space of preregular maps. In: Quaestiones Mathematicae. 2011 ; Vol. 34. pagg. 113-117.
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