Banach Lattices of Continuous Banach Lattice-Valued Functions

Banach Lattices of Continuous Banach Lattice-Valued Functions

This paper studies the Banach lattice structure of some spaces of continuous functions taking values in a Banach lattice. We determine when they satisfy various kinds of order theoretic completeness conditions and what properties the norm in such a Banach lattice may possess and describe their centr...

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Veröffentlicht in:Journal of mathematical analysis and applications 1996-02, Vol.198 (1), p.121-136
Hauptverfasser: Ercan, Z., Wickstead, A.W.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Sciences and techniques of general use
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Zusammenfassung:This paper studies the Banach lattice structure of some spaces of continuous functions taking values in a Banach lattice. We determine when they satisfy various kinds of order theoretic completeness conditions and what properties the norm in such a Banach lattice may possess and describe their centres. Various extension and separation results known for spaces of real-valued continuous functions are generalised to this setting.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1996.0072