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)

 
 

 

Alternating sequences with nonpositive operators


Author: M. A. Akcoglu
Journal: Proc. Amer. Math. Soc. 104 (1988), 1124-1130
MSC: Primary 47A35; Secondary 28D05, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0943791-8
MathSciNet review: 943791
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ ({T_n})$ be a sequence of linear operators acting on complex valued functions on a $ \sigma $-finite measure space. Assume that each $ {T_n}$ contracts all the $ p$-norms, $ 1 \leq p \leq \infty ({\text{i}}{\text{.e}}{\text{.}}{\left\Vert {{T_n}} \right\Vert _p} \leq 1)$. It is shown that a.e. $ {\lim _n}T_1^ * \cdots T_n^ * {T_n} \cdots {T_1}f$ exists for each $ {L_p}$ function $ f,1 < p < \infty $.


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

  • [1] M. A. Akcoglu and A. Brunel, Contractions of $ {L_1}$ spaces, Trans. Amer. Math. Soc. 155 (1971), 315-325. MR 0276439 (43:2186)
  • [2] M. A. Akcoglu and L. Sucheston, Dilations of positive contractions, Canad. Math. Bull. 20 (1977), 285-292. MR 0458230 (56:16433)
  • [3] -, Pointwise convergence of alternating sequences, Canad. J. Math. (to appear). MR 960598 (90b:47017)
  • [4] U. Krengel, Ergodic theorems, de Gruyter Studies in Math., vol. 6, 1985. MR 797411 (87i:28001)
  • [5] G. C. Rota, An "Alternierende Verfahren" for general positive operators, Bull. Amer. Math. Soc. 68 (1962), 95-102. MR 0133847 (24:A3671)
  • [6] N. Starr, Operator limit theorems, Trans. Amer. Math. Soc. 121 (1966), 90-115. MR 0190757 (32:8167)
  • [7] E. Stein, On the maximal ergodic theorem, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1894-1897. MR 0131517 (24:A1367)
  • [8] -, Topics in harmonic analysis, Princeton Univ. Press, 1970.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35, 28D05, 47B38

Retrieve articles in all journals with MSC: 47A35, 28D05, 47B38


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943791-8
Keywords: Contractions of $ {L_p}$ spaces, maximal inequalities
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society