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The semi-M property for normed Riesz spaces. (English) Zbl 0345.46009


MSC:

46A40 Ordered topological linear spaces, vector lattices
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B99 Normed linear spaces and Banach spaces; Banach lattices
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References:

[1] T. Ando : Linear functionals on Orlicz spaces . Nieuw Archief voor Wiskunde (3) VIII (1960) 1-16. · Zbl 0129.08001
[2] E. De Jonge : A pair of mutually associate Banach function spaces . Proc. Kon. Ned. Akad. Wet. 77 (1974) 148-156. · Zbl 0277.46021
[3] E. De Jonge : The triangle equality for positive singular functionals on some classes of normed Köthe spaces I and II . Proc. Kon. Ned. Akad. Wet. 78 (1975) 48-69. · Zbl 0294.46017
[4] E. De Jonge : Representation of linear functionals on a class of normed Köthe spaces . J. Functional Analysis 23(2) (1976) 119-134. · Zbl 0336.46035
[5] W.A.J. Luxemburg : Rearrangement-invariant Banach function spaces . Queen’s papers in pure and applied Mathematics 10 (1967) 83-144. · Zbl 0162.44701
[6] W.A.J. Luxemburg and A.C. Zaanen : Notes on Banach function spaces VI and VII . Proc. Kon. Ned. Akad. Wet. 66 (1963) 655-681. · Zbl 0147.11001
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[8] W.A.J. Luxemburg and A.C. Zaanen : Riesz spaces I . Amsterdam (1971). · Zbl 0231.46014
[9] M.M. Rao : Linear functionals on Orlicz spaces: General theory . Pac. Journal of Math. 25 (3) (1968) 553-585. · Zbl 0164.43601
[10] M.S. Steigerwalt and A.J. White : Some function spaces related to L p spaces . Proc. London Math. Soc. (3) XXII (1971) 137-163. · Zbl 0217.16502
[11] A.C. Zaanen : Linear analysis . Amsterdam (1953). · Zbl 0053.25601
[12] A.C. Zaanen : Integration , Amsterdam (1967). · Zbl 0175.05002
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