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Bombal Gordón, Fernando
(1980)
*On the space Lp(μ,X). (Spanish: Sobre el espacio Lp(μ,X)).*
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 74
(1).
pp. 131-135.
ISSN 0034-0596

PDF
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Official URL: http://www.rac.es/4/4_7_1.php?pid=Revistas:REV_20091030_00408&pageNum=1

## Abstract

Letting X be a Banach space, (S,μ,Σ) a space of finite measure, 1<p<∞ , and L p (μ,X) the space of functions from S into X with |f| p integrable, the author studies the dual pair (L p (μ,X),L q (μ,X ′ )). He gives necessary conditions, which are also sufficient if X has the Radon-Nikodým property, in order that a subset of L p (μ,X) be σ(L p (μ,X),L q (μ,X ′ )) -relatively sequentially compact and shows that L p (μ,X) is σ(L p (μ,X),L q (μ,X ′ )) sequentially complete for every finite measure μ if and only if X is weakly sequentially complete and has the Radon-Nikodým property.

Item Type: | Article |
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Uncontrolled Keywords: | Lp-spaces; Orlicz spaces; Köthe function spaces; Lorentz spaces; rearrangement invariant spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory Sciences > Mathematics > Differential equations |

ID Code: | 17971 |

Deposited On: | 25 Jan 2013 09:46 |

Last Modified: | 02 Aug 2018 07:50 |

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