Articles

A note on the Banach space of preregular maps

Published in: Quaestiones Mathematicae
Volume 34 , issue 1 , 2011 , pages: 113–117

DOI: 10.2989/16073606.2011.570305

Author(s): CoenraadC.A. Labuschagne* , South Africa , Valeria Marraffat† Dipartimento di Matematica ed Applicazioni,

Keywords: 46B42 , 47B60 , 74B65 , 46B42 , 47B60 , 74B65

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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 (E,F) of all those linear maps T : E → F for which there exists a constant K such that for all finite sequences . We show that, if (E,F), and the spaces (E,F) of θ-map and (E,F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach spaces.

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