Abstract
We give a very short proof of the theorem concerning long strings of projections mentioned in the title. The nature of the proof is such that, for example, a result of Gul’ko follows easily.
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References
D. Amir and J. Lindenstrauss,The structure of weakly compact sets in Banach spaces, Ann. of Math.88 (1968), 35–46.
S. Argyros and S. Negrepontis,On weakly countably determined spaces of continuous functions. Proc. Am. Math. Soc.87 (1983), 731–736.
N. Bourbaki,Topologie général. Actualités Sci. Ind., Paris, 1942–1949.
R. Engelking,General Topology, PWN, Warszawa, 1977.
S. P. Gul’ko,On the structure of spaces of continuous functions and their complete paracompactness, Russian Math. Surveys34 (1979), 36–44.
S. Mercourakis,On weakly countably determined Banach spaces, Trans. Am. Math. Soc., to appear.
M. A. Naimark,Normed Rings, Noordhoff, Gromingen, 1964.
S. Negrepontis,Banach spaces and topology, inHandbook of Set Theoretic Topology, North-Holland, Amsterdam, 1984.
I. Namioka and R. F. Wheeler,Gul’ko’s proof of the Amir-Lindenstrauss theorem, Contemp. Math.52 (1986), 113–120.
R. Pol,On Pointwise and Weak Topology in Function Spaces, University of Warsaw, 1984.
J. D. Pryce,A device of R. J. Whitley applied to pointwise compactness in spaces of continuous functions, Proc. London Math. Soc.23 (1971), 532–536.
C. Stegall,Generalizations of a theorem of Namioka, Proc. Am. Math. Soc.102 (1988), 559–564.
M. Talagrand,Espaces de Banach faiblement k-analytique, Ann. of Math.110 (1979), 407–438.
L. Vasak,On one generalization of weakly compactly generated Banach spaces, Studia Math.70 (1981), 11–19.
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Stegall, C. A proof of the theorem of amir and lindenstrauss. Israel J. Math. 68, 185–192 (1989). https://doi.org/10.1007/BF02772660
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DOI: https://doi.org/10.1007/BF02772660