Sequential convergence in the order duals of certain classes of riesz spaces

P. G. Dodds

doi:10.1090/S0002-9947-1975-0358282-0

Sequential convergence in the order duals of certain classes of riesz spaces

P. G. Dodds

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind ocomplete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.

Original language	English
Pages (from-to)	391-403
Number of pages	13
Journal	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume	203
DOIs	https://doi.org/10.1090/S0002-9947-1975-0358282-0
Publication status	Published - 1975

Keywords

Archimedean Riesz spaces
Order dual
Principal projection property
Sequential convergence
Weak compactness

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abstract = "Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind ocomplete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.",

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AB - Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind ocomplete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.

KW - Archimedean Riesz spaces

KW - Order dual

KW - Principal projection property

KW - Sequential convergence

KW - Weak compactness

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SN - 0002-9947

ER -

Sequential convergence in the order duals of certain classes of riesz spaces

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Keywords

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