A note on the Banach space of preregular maps

Valeria Marraffa, Coenraad C. A. Labuschagne

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)113-117
Number of pages5
JournalQuaestiones Mathematicae
Volume34
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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