Complex vector lattices via functional completions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Buskes, G.¹  Schwanke, C.² 

[1] Univ Mississippi, Dept Math, University, MS 38677 USA

[2] North West Univ, Unit BMI, Private Bag X6001, ZA-2520 Potchefstroom, South Africa

关键词: Vector lattices;    Complexifications;    Fremlin tensor product;    Multilinear maps;    Order bounded variation;   

DOI  :  10.1016/j.jmaa.2015.09.080

来源: Elsevier

【 摘 要 】

We show that the Fremlin tensor product C(X)(circle times) over barC(Y) is not square mean complete when X and Y are uncountable metrizable compact spaces. This motivates the definition of complexification of Archimedean vector lattices, the Fremlin tensor product of Archimedean complex vector lattices, and a theory of powers of Archimedean complex vector lattices. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free