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On finite elements in vector lattices and Banach lattices

✍ Scribed by Z. L. Chen; M. R. Weber

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
124 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In Archimedean vector lattices we show that each element of the band generated by a finite element is also finite. In vector lattices with the (PPP) and in Banach lattices we obtain some characterizations of finite elements by using the generalized order units for principal bands. In the case of Banach lattices with order continuous norm the ideal of all finite elements coincides with the linear span of all atoms. Some other related results and applications are included. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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