Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T16:11:58.433Z Has data issue: false hasContentIssue false
  • English
  • Français

Contractions with Fixed Points and Conditional Expectation

Published online by Cambridge University Press:  20 November 2018

A. N. Al-Hussaini
A. N. Al-Hussaini*
Affiliation:
University of Alberta and University of Illinois
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let (Ω, α, μ) be a σ-finite measure space. By Lp(Ω, α, μ) or Lp for short we denote the usual Banach space of pth power μ-integrable functions on Ω if 1≤p<+ ∞ and μ-essentially bounded functions on Ω, if p= +∞. In section (2) we characterize conditional expectation, by a method different than those used previously. Modulus of a given contraction is discussed in section (3). If the given contraction has a fixed point, then its modulus has a simple form (theorem 3.2).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 475 - 478
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Al-Hussaini, A. N., On characterization of conditional expectation, Canad. Math. Bull, vol. 16 (2) 1973.Google Scholar
2. Ando, T., Contractive projections in Lp space, Pacific Journal of Math. vol. 17 (3) 1966.Google Scholar
3. Chacon, R. V. and Ornstein, D., A general ergodic theorem, Illinois J. Math. (1960).Google Scholar
4. Chacon, R. Y. and Krengel, U., Linear modulus of linear operators, Proc. Amer. Math. Soc. (1964).Google Scholar
5. Chacon, R. V., Convergence of operator averages, Proceeding Tulane Symp. Ergodic theory (1962) pp. 89–120.Google Scholar
6. Douglas, R. G., Contractive projections on an L1-space, Pacific J. Math. (1965).Google Scholar