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Representation of linear functionals on a class of normed Köthe spaces. (English) Zbl 0336.46035


MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A40 Ordered topological linear spaces, vector lattices
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[1] Ando, T., Linear functionals on Orlicz spaces, Nieuw Archief voor de wiskunde, 8, No. 3, 1-16 (1960), (3) · Zbl 0129.08001
[2] Dunford, N.; Schwartz, J. T., Linear Operators I (1958), Interscience: Interscience New York
[3] Gretsky, N. E., Representation theorems on Banach function spaces, Mem. Amer. Math. Soc., 84 (1968) · Zbl 0181.14701
[4] de Jonge, E., Singular functionals on Köthe spaces, Thesis (1973), Leiden · Zbl 0294.46018
[5] de Jonge, E., A pair of mutually associate Banach function spaces, (Proc. Kon. Neder. Akad. Wet., 77 (1974)), 148-156 · Zbl 0277.46021
[6] E. de Jonge\(M Comp. Math. \); E. de Jonge\(M Comp. Math. \) · Zbl 0345.46009
[7] Luxemburg, W. A.J; Zaanen, A. C., Riesz Spaces I (1971), North-Holland: North-Holland Amsterdam · Zbl 0231.46014
[8] Rao, M. M., Linear functionals on Orlicz spaces: General theory, Pacific. J. Math., 25, No. 3, 553-585 (1968) · Zbl 0164.43601
[9] Yosida, K.; Hewitt, E., Finitely additive measures, Trans. Amer. Math. Soc., 72, 46-66 (1952) · Zbl 0046.05401
[10] Zaanen, A. C., Integration (1967), North-Holland: North-Holland Amsterdam · Zbl 0175.05002
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