Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A cocycle theorem with an application
to Rosenthal sets

Author: Peter Schwartz
Journal: Proc. Amer. Math. Soc. 124 (1996), 3689-3698
MSC (1991): Primary 47A99, 42A16, 42A55
MathSciNet review: 1328377
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For certain Markov operators $T$ we show that bounded cocycles with respect to $T$ are coboundaries. This result is applied to show that certain translation invariant subspaces of functions on the unit circle have unexpected regularity properties.

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

  • [Bl1] R. C. Blei, on trigonometric series associated with separable, translation invariant subspaces of $\mathbf L^\infty (G)$, Trans. Amer. Math. Soc. 173 (1972), 491-499. MR 47:2269
  • [Bl2] -, A simple diophantine condition in harmonic analysis, Studia Math. 52 (1974), 195-202. MR 57:10368
  • [Bl3] -, Rosenthal sets that cannot be sup-norm partitioned and an application to tensor products, Colloq. Math. 37 (1977), 295-298. MR 58:2025
  • [FIS] S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear algebra, Prentice Hall, 1979. MR 80i:15001
  • [Fo] S. R. Foguel, Ergodic decomposition of a topological space, Israel J. Math. 7 (1969), 164-167. MR 40:2815
  • [GH] W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, 1955, pp. 135-136. MR 17:650e
  • [Kr] Ulrich Krengel, Ergodic theorems, Walter de Gruyter, 1985. MR 87i:28001
  • [LS] M. Lin and R. Sine, Ergodic theory and the functional equation $(I-T)x=y$, J. Operator Theory 10 (1983), 153-166. MR 84m:47015
  • [LR] J. M. Lopez and K. A. Ross, Sidon sets, Marcel Dekker, New York, 1975. MR 55:13173
  • [Me] P. A. Meyer, Probability and potentials, Blaisdell, Waltham, MA, 1966. MR 34:5119
  • [PS1] L. Pigno and S. Saeki, On the spectra of almost periodic functions, Indiana Univ. Math. J. 25 (1976), 191-194. MR 53:11312
  • [PS2] -, Almost periodic functions and certain lacunary sets, Kansas State University Technical Report 42, 1974.
  • [Ro] H. P. Rosenthal, On trigonometric series associated with weak$^*$ closed subspaces of continuous functions, J. Math. Mech. 17 (1967), 485-490. MR 35:7064
  • [St] Stromberg, An introduction to classical real analysis, Wadsworth International Group, 1981. MR 82c:26002

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A99, 42A16, 42A55

Retrieve articles in all journals with MSC (1991): 47A99, 42A16, 42A55

Additional Information

Peter Schwartz
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Received by editor(s): February 17, 1994
Received by editor(s) in revised form: March 25, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society