On compactness in functional analysis
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- by Robert G. Bartle
- Trans. Amer. Math. Soc. 79 (1955), 35-57
- DOI: https://doi.org/10.1090/S0002-9947-1955-0073938-2
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References
- C. Arzelà, Intorno alla continuità della somma d’infinità di funzioni continue, Rend. dell’Accad. di Bologna (1883-1884) pp. 79-84.
—, Sulle funzioni di linee, Mem. dell’Accad. di Bologna Ser. V, vol. 5 (1885) pp. 225-244.
G. Ascoli, Sulle curve limiti di una varietà di curve, Mem. Accad. Lincei Ser. III, vol. 18 (1884) pp. 521-586.
S. Banach, Théorie des opérations linéaires, Monografje Matematyczne, vol. 1, Warsaw, 1932.
- D. G. Bourgin, Some properties of Banach spaces, Amer. J. Math. 64 (1942), 597–612. MR 8116, DOI 10.2307/2371707
- W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217–240. MR 36455, DOI 10.1090/S0002-9947-1949-0036455-9
- W. F. Eberlein, Weak compactness in Banach spaces. I, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 51–53. MR 21239, DOI 10.1073/pnas.33.3.51
- Vera. Gantmacher, Über schwache totalstetige Operatoren, Rec. Math. [Mat. Sbornik] N.S. 7 (49) (1940), 301–308 (German, with Russian summary). MR 0003471 I. Gelfand, Abstrakte Funktionen und lineare Operatoren, Rec. Math. (Mat. Sbornik) vol. 4(46) (1938) pp. 235-284.
- H. H. Goldstine, Weakly complete Banach spaces, Duke Math. J. 4 (1938), no. 1, 125–131. MR 1546039, DOI 10.1215/S0012-7094-38-00410-7
- A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. 74 (1952), 168–186 (French). MR 47313, DOI 10.2307/2372076
- Shizuo Kakutani, A proof of Schauder’s theorem, J. Math. Soc. Japan 3 (1951), 228–231. MR 44019, DOI 10.2969/jmsj/00310228
- J. L. Kelley, Convergence in topology, Duke Math. J. 17 (1950), 277–283. MR 36982 S. Mazur, Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Mathematica vol. 2 (1930) pp. 7-9.
- Masahiro Nakamura, Complete continuities of linear operators, Proc. Japan Acad. 27 (1951), 544–547. MR 49482
- R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1940), 516–541. MR 4094, DOI 10.1090/S0002-9947-1940-0004094-3
- R. S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108–136. MR 7938, DOI 10.2307/2371776 J. Schauder, Über lineare, vollstetige Funktionaloperationen, Studia Mathematica vol. 2 (1930) pp. 183-196.
- G. Sirvint, Schwache Kompaktheit in den Banachschen Räumen, C. R. (Doklady) Acad. Sci. URSS (N.S.) 28 (1940), 199–202 (German). MR 0003445
- G. Sirvint, Weak compactness in Banach spaces, Studia Math. 11 (1950), 71–94. MR 49481, DOI 10.4064/sm-11-1-71-94 V. Šmulian, Sur les ensembles compacts et faiblement compacts dans l’espace du type $(B)$, Rec. Math. (Mat. Sbornik) vol. 12(54) (1943) pp. 91-97.
- M. H. Stone, On the compactification of topological spaces, Ann. Soc. Polon. Math. 21 (1948), 153–160. MR 0026316
Bibliographic Information
- © Copyright 1955 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 79 (1955), 35-57
- MSC: Primary 46.2X
- DOI: https://doi.org/10.1090/S0002-9947-1955-0073938-2
- MathSciNet review: 0073938