A note on the Banach space of preregular maps

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 !-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space L!(E, F) of all those linear maps T : E " F for which there exists a constant K such that #!n i=1 |Txi|# $ K#!n i=1 |xi| # for all finite sequences x1, . . . , xn % E. We show that, if L!(E, F), and the spaces L"(E, F) of !-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)1-5
Numero di pagine5
RivistaQuaestiones Mathematicae
Volume34
Stato di pubblicazionePublished - 2011

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Banach space
L-space
Banach Lattice
Linear map
Norm

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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A note on the Banach space of preregular maps. /.

In: Quaestiones Mathematicae, Vol. 34, 2011, pag. 1-5.

Risultato della ricerca: Article

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