Abstract ergodic theorems and weak almost periodic functions
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References
- L. Alaoglu and G. Birkhoff, General ergodic theorems, Ann. of Math. (2) 41 (1940), 293–309. MR 2026, DOI 10.2307/1969004 S. Banach, Théorie des opérations linéaires, Warsaw, 1932. A. S. Besicovitch, Almost periodic functions, Cambridge, England, 1932. S. Bochner, Vorlesungen über Fouriersche Integrale, Leipzig, 1932.
- Harald Bohr and Erling Følner, On some types of functional spaces. A contribution to the theory of almost periodic functions, Acta Math. 76 (1945), 31–155. MR 13443, DOI 10.1007/BF02547156
- D. G. Bourgin, Linear topological spaces, Amer. J. Math. 65 (1943), 637–659. MR 9104, DOI 10.2307/2371871
- J. W. Calkin, Abstract symmetric boundary conditions, Trans. Amer. Math. Soc. 45 (1939), no. 3, 369–442. MR 1501997, DOI 10.1090/S0002-9947-1939-1501997-7
- Mahlon M. Day, Operation in Banach spaces, Trans. Amer. Math. Soc. 51 (1942), 583–608. MR 6613, DOI 10.1090/S0002-9947-1942-0006613-1
- Mahlon Day M., Ergodic theorems for Abelian semigroups, Trans. Amer. Math. Soc. 51 (1942), 399–412. MR 6614, DOI 10.1090/S0002-9947-1942-0006614-3
- Nelson Dunford, Spectral theory. I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185–217. MR 8642, DOI 10.1090/S0002-9947-1943-0008642-1
- Nelson Dunford, Spectral theory, Bull. Amer. Math. Soc. 49 (1943), 637–651. MR 8643, DOI 10.1090/S0002-9904-1943-07965-7
- Nelson Dunford and D. S. Miller, On the ergodic theorem, Trans. Amer. Math. Soc. 60 (1946), 538–549. MR 18359, DOI 10.1090/S0002-9947-1946-0018359-8
- Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 2020, DOI 10.1090/S0002-9947-1940-0002020-4
- 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
- W. F. Eberlein, Abstract ergodic theorems, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 43–47. MR 23460, DOI 10.1073/pnas.34.2.43
- M. Eidelheit, On isomorphisms of rings of linear operators, Studia Math. 9 (1940), 97–105 (English, with Ukrainian summary). MR 4725, DOI 10.4064/sm-9-1-97-105
- I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197–213 (English, with Russian summary). MR 0009426
- Roger Godement, Les fonctions de type positif et la théorie des groupes, Trans. Amer. Math. Soc. 63 (1948), 1–84 (French). MR 23243, DOI 10.1090/S0002-9947-1948-0023243-1
- W. H. Gottschalk, Almost periodicity, equi-continuity and total boundedness, Bull. Amer. Math. Soc. 52 (1946), 633–636. MR 16551, DOI 10.1090/S0002-9904-1946-08611-5
- Einar Hille, Remarks on ergodic theorems, Trans. Amer. Math. Soc. 57 (1945), 246–269. MR 12212, DOI 10.1090/S0002-9947-1945-0012212-0
- D. H. Hyers, Linear topological spaces, Bull. Amer. Math. Soc. 51 (1945), 1–21. MR 12205, DOI 10.1090/S0002-9904-1945-08273-1
- Shizuo Kakutani, Two fixed-point theorems concerning bicompact convex sets, Proc. Imp. Acad. Tokyo 14 (1938), no. 7, 242–245. MR 1568507
- Shizuo Kakutani, Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994–1024. MR 5778, DOI 10.2307/1968778
- Yukiyosi Kawada, Über den Mittelwert der messbaren fastperiodischen Funktionen auf einer Gruppe, Proc. Imp. Acad. Tokyo 19 (1943), 264–266 (German). MR 14098 W. Maak, Eine neue Definition der fastperiodischen Funktionen, Abh. Math. Sem. Hamburgischen Univ. vol. 11 (1936) pp. 240-244.
- J. v. Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445–492. MR 1501752, DOI 10.1090/S0002-9947-1934-1501752-3
- R. S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108–136. MR 7938, DOI 10.2307/2371776
- D. A. Raikov, Harmonic analysis on commutative groups with the Haar measure and the theory of characters, Trav. Inst. Math. Stekloff 14 (1945), 86 (Russian, with English summary). MR 0017285 F. Riesz, Some mean ergodic theorems, J. London Math. Soc. vol. 13 (1938) pp. 274-278.
- V. Šmulian, On some problems of the functional analysis, C. R. (Doklady) Acad. Sci. URSS (N.S.) 38 (1943), 157–159. MR 0008637
- Béla de Sz. Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 152–157. MR 22309
- John W. Tukey, Convergence and Uniformity in Topology, Annals of Mathematics Studies, No. 2, Princeton University Press, Princeton, N. J., 1940. MR 0002515 A. Weil, L’integration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, no. 869, Paris, 1940.
- Kôsaku Yosida and Shizuo Kakutani, Operator-theoretical treatment of Markoff’s process and mean ergodic theorem, Ann. of Math. (2) 42 (1941), 188–228. MR 3512, DOI 10.2307/1968993 A. Zygmund, Trigonometrical series, Warsaw, 1935.
Additional Information
- © Copyright 1949 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 67 (1949), 217-240
- MSC: Primary 46.3X
- DOI: https://doi.org/10.1090/S0002-9947-1949-0036455-9
- MathSciNet review: 0036455