Filter, Wolfgang Atomical and atomfree elements of a Riesz space. (English) Zbl 0659.46004 Arch. Math. 52, No. 6, 580-587 (1989). A band decomposition of Riesz spaces with separating order continuous dual is investigated which contains the well-known decomposition of measures into an atomical and an atomfree part as a special case. Reviewer: W.Filter Cited in 3 Documents MSC: 47A40 Scattering theory of linear operators Keywords:band decomposition of Riesz spaces with separating order continuous dual; decomposition of measures into an atomical and an atomfree part PDFBibTeX XMLCite \textit{W. Filter}, Arch. Math. 52, No. 6, 580--587 (1989; Zbl 0659.46004) Full Text: DOI References: [1] C. D.Aliprantis and O.Burkinshaw, Locally solid Riesz spaces. New York-San Francisco-London 1978. [2] W.Filter, Representations of Riesz spaces as spaces of measures. Preprint. · Zbl 0803.46009 [3] W. Filter, A note on Archimedean Riesz spaces and their extended order duals. Libertas Math.6, 101-106 (1986). · Zbl 0612.46007 [4] W. A. J. Luxemburg andJ. J. Masterson, An extension of the concept of the order dual of a Riesz space. Canad. J. Math.19, 488-498 (1967). · Zbl 0147.11101 · doi:10.4153/CJM-1967-041-6 [5] W. A. J.Luxemburg and A. C.Zaanen, Riesz spaces I. Amsterdam-London 1971. · Zbl 0231.46014 [6] A. C.Zaanen, Riesz spaces II. Amsterdam-New York-Oxford 1983. · Zbl 0519.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.