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Wickstead, A. W.

Representation and duality of multiplication operators on archimedean Riesz spaces. (English) Zbl 0381.47021

Compos. Math. 35, 225-238 (1977).
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Cited in 7 Reviews
Cited in 34 Documents

MSC:

47B60 Linear operators on ordered spaces
47L05 Linear spaces of operators
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46A40 Ordered topological linear spaces, vector lattices
46E05 Lattices of continuous, differentiable or analytic functions
46B42 Banach lattices
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References:

[1] S.J. Bernau : Unique representation of Archimedean lattice groups and normal Archimedean lattice rings . Proc. London Math. Soc. (3) 15 (1965) 599-631. · Zbl 0134.10802 · doi:10.1112/plms/s3-15.1.599
[2] A. Bigard : Les orthomorphismes d’un espace réticulé Archimédien . Indag. Math. 34 (1972) 236-246. · Zbl 0235.06008
[3] A. Bigard and K. Keimel : Sur les endomorphismes conservant les polaires d’un groupe réticulé Archimédien . Bull. Soc. Math. France 97 (1969) 381-398. · Zbl 0215.34203 · doi:10.24033/bsmf.1690
[4] R.C. Buck : Multiplication operators . Pacific J. Maths. 11 (1961) 95-104. · Zbl 0102.32901 · doi:10.2140/pjm.1961.11.95
[5] P.F. Conrad and J.E. Diem : The ring of polar preserving endomorphisms of an abelian lattice ordered group . Illinois J. Math. 15 (1971) 224-240. · Zbl 0213.04002
[6] J. Dixmier : Sur certains espaces considérés par M.H. Stone . Summa Bras. Math. 2 (1951) 151-182. · Zbl 0045.38002
[7] H.O. Flösser : Die Orthomorphismen einiger lokalkonvexer Vektorverbände . Preprint.
[8] D.H. Fremlin : Abstract Köthe spaces II . Proc. Cam. Phil. Soc. 63 (1967) 951-956. · Zbl 0179.17005
[9] A.C. Zaanen : Examples of Orthomorphisms . J. Approx. Thy. 13 (1975) 192-204. · Zbl 0293.47010 · doi:10.1016/0021-9045(75)90052-0
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