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Pointwise compactness in spaces of functions and R. C. James theorem. (English) Zbl 0274.46019


MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
46A03 General theory of locally convex spaces
46A08 Barrelled spaces, bornological spaces
46A25 Reflexivity and semi-reflexivity
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References:

[1] De Wilde, M., Houet, C.: On increasing sequences of absolutely convex sets in locally convex spaces. Math. Ann.192, 257-261 (1971) · Zbl 0212.14101 · doi:10.1007/BF02075355
[2] De Wilde, M.: Quelques propriétés de permanence des espaces à réseau. Bull. Soc. Roy. Sc. Liège.39, 5-6, 240-248 (1970)
[3] Grothendieck, A.: Critères de compacité dans les espaces fonctionnels généraux. Am. J. Math.74, 168-186 (1952) · Zbl 0046.11702 · doi:10.2307/2372076
[4] James, R. C.: Weakly compact sets. Trans. A.M.S.113, 1, 129-140 (1964) · Zbl 0129.07901 · doi:10.1090/S0002-9947-1964-0165344-2
[5] Kelley, J. L., Namioka, I.: Linear topological spaces. Princeton N.J.: Van Nostrand 1963 · Zbl 0115.09902
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[7] Pryce, J.D.: Weak compactness in locally convex spaces. Proc. A.M.S.17, 1, 148-155 (1966) · Zbl 0141.11702 · doi:10.1090/S0002-9939-1966-0190695-2
[8] Pryce, J.D.: A device of R. J. Whitley’s applied to pointwise compactness in spaces of continuous functions. Proc. London Math. Soc.23, 532-546 (1971) · Zbl 0221.46012 · doi:10.1112/plms/s3-23.3.532
[9] Rainwater, J.: Weak convergence of bounded sequences. Proc. A.M.S.14, 199 (1963) · Zbl 0117.08302
[10] Simons, S.: A convergence theorem with boundary. Pacific J. Math.40, 703-708 (1972) · Zbl 0237.46012
[11] Simons, S.: Maximinimax, minimax, and antiminimax theorems and a result of R. C. James. Pacific J. Math.40, 709-718 (1971) · Zbl 0237.46013
[12] Simons, S.: On Ptak’s combinatorial lemma. Pacific J. Math.40, 719-722 (1972) · Zbl 0237.46014
[13] Simons, S.: A theorem on lattice ordered groups, results of Ptak, Namioka and Banach, and a frontended proof of Lebesgue’s theorem. Pacific J. Math.20, 149-153 (1967) · Zbl 0146.04901
[14] Tweddle, I.: Weak compactness in locally convex spaces. Glasgow Math. J.9, (2), 123-127 (1968) · Zbl 0159.41802 · doi:10.1017/S0017089500000409
[15] Whitley, R.: An elementary proof of the Eberlein-Smulian theorem. Math. Ann.172, 116-118 (1967) · Zbl 0146.36301 · doi:10.1007/BF01350091
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