Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A fixed point theorem-free approach to weak almost periodicity


Author: William A. Veech
Journal: Trans. Amer. Math. Soc. 177 (1973), 353-362
MSC: Primary 54H20; Secondary 43A60
DOI: https://doi.org/10.1090/S0002-9947-1973-0343254-0
MathSciNet review: 0343254
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we present a generalization of the Eberlein, de Leeuw and Glicksberg decomposition theorem for weakly almost periodic functions which does not rely on any fixed point theorem for its proof. A generalization of the Ryll-Nardzewski fixed point theorem is given.


References [Enhancements On Off] (What's this?)

  • [1] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. (2) 88 (1968), 35-46. MR 37 #4562. MR 0228983 (37:4562)
  • [2] K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63-97. MR 24 #A1632. MR 0131784 (24:A1632)
  • [3] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [4] W. F. Eberlein, Abstract ergodic theorems and weakly almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217-240. MR 12, 112. MR 0036455 (12:112a)
  • [5] R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94 (1960), 272-281. MR 33 #A961. MR 0123636 (23:A961)
  • [6] -, Distal transformation groups, Pacific J. Math. 8 (1958), 401-405. MR 21 #96. MR 0101283 (21:96)
  • [7] -, Lectures on topological dynamics, Benjamin, New York, 1969. MR 42 #2463. MR 0267561 (42:2463)
  • [8] H. Furstenberg, The structure of distal flows, Amer. J. Math. 85 (1963), 477-515. MR 28 #602. MR 0157368 (28:602)
  • [9] R. Godement, Les fonctions de type positif et la théorie des groupes, Trans. Amer. Math. Soc. 63 (1948), 1-84. MR 9, 327. MR 0023243 (9:327b)
  • [10] A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. 74 (1952), 168-186. MR 13, 857. MR 0047313 (13:857e)
  • [11] -, Sur les applications linéaires faiblement compactes d'espaces du type $ C(K)$, Canad. J. Math. 5 (1953), 129-173. MR 15, 438. MR 0058866 (15:438b)
  • [12] F. Hahn, A fixed-point theorem, Math. Systems Theory 1 (1967), 55-57. MR 34 #8202. MR 0208392 (34:8202)
  • [13] J. L. Kelley, General topology, Van Nostrand, Princeton, N. J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [14] A. Knapp, Decomposition theorem for bounded uniformly continuous functions on a group, Amer. J. Math. 88 (1966), 902-914. MR 34 #8212. MR 0208402 (34:8212)
  • [15] I. Namioka, Neighborhoods of extreme points, Israel J. Math. 5 (1967), 145-152. MR 36 #4323. MR 0221271 (36:4323)
  • [16] -, Right topological groups, distal flows, and a fixed point theorem (preprint).
  • [17] H. P. Rosenthal, On injective Banach spaces and the spaces $ {L^\infty }(\mu )$ for finite measures $ \mu $, Acta Math. 124 (1970), 205-248. MR 41 #2370. MR 0257721 (41:2370)
  • [18] C. Ryll-Nardzewski, On fixed points of semigroups of endomorphisms of linear spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. II: Contributions to Probability Theory, part 1, Univ. of California Press, Berkeley, Calif., 1967, pp. 55-61. MR 35 #5977. MR 0215134 (35:5977)
  • [19] W. Veech, Generalizations of almost periodic functions, Mimeographed Notes, 58 pp.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54H20, 43A60

Retrieve articles in all journals with MSC: 54H20, 43A60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0343254-0
Keywords: Weakly almost periodic function, fixed point theorem, Eberlein compact
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society