Complex vector lattices via functional completions
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Buskes, G.
Schwanke, C.
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Elsevier
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We show that the Fremlin tensor product View the MathML sourceC(X)⊗¯C(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
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Buskes, G. & Schwanke, C. 2016. Complex vector lattices via functional completions. Journal of mathematical analysis and applications, 434(2):1762-1778. [https://doi.org/10.1016/j.jmaa.2015.09.080]