Abstract
It is proved that for uncountableΓ,c 0(Γ) has no quasicomplement inm(Γ).
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References
D. Amir and J. Lindenstrauss,The structure of weakly compact sets in Banach spaces., to appear in Ann. of Math.
W. G. Bade,Extension of interpolation sets, to appear.
M. M. Day,Normed linear spaces, Springer-Verlag, Berlin, 1958.
L. Gillman and M. Jerison,Rings of continuous functions, Van Nostrand, Princeton, 1960.
A. Grothendieck,Sur les applications linéaires faiblement compacte d’espaces du type C(K), Canadian J. Math.5 (1953), 129–173.
J. Lindenstrauss,On a theorem of Murray and Mackey, Anais de Acad. Brasileira Cien.39 (1967), 1–5.
—————,On the extension of operators with range in a C(K) space, Proc. Amer. Math. Soc.15 (1964), 218–225.
-----,Weakly compact sets — their topological properties and the Banach spaces they generate, to appear in the Proc. Symposium on infinite dimensional topology, L.S.U. 1967.
G. Mackey,Note on a theorem of Murray, Bull. Amer. Math. Soc.52 (1946), 322–325.
F. J. Murray,Quasi complements and closed projections in reflexive Banach spaces, Trans. Amer. Math. Soc.58 (1945), 77–95.
F. L. Seever,Measures on F-spaces, Thesis, University of California, Berkley, 1963.
Z. Semadeni,On weak convergence of measures on σ-complete Boolean algebras, Colloq. Math. 12 (1964), 229–233.
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Research supported by the National Science Foundation, U.S.A.
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Lindenstrauss, J. On subspaces of Banach spaces without quasicomplements. Israel J. Math. 6, 36–38 (1968). https://doi.org/10.1007/BF02771603
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DOI: https://doi.org/10.1007/BF02771603