### Abstract

Lingua originale | English |
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pagine (da-a) | 1-5 |

Numero di pagine | 5 |

Rivista | Quaestiones Mathematicae |

Volume | 34 |

Stato di pubblicazione | Published - 2011 |

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### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

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

Risultato della ricerca: Article

*Quaestiones Mathematicae*, vol. 34, pagg. 1-5.

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TY - JOUR

T1 - A note on the Banach space of preregular maps

AU - Marraffa, Valeria

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Banach lattice, preregular operator, regular operator.

UR - http://hdl.handle.net/10447/55479

M3 - Article

VL - 34

SP - 1

EP - 5

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

SN - 1607-3606

ER -