Alternating sequences and induced operators
Authors:
M. A. Akcoglu and R. E. Bradley
Journal:
Trans. Amer. Math. Soc. 325 (1991), 765-791
MSC:
Primary 47A35; Secondary 47B38, 47B60, 47B65
DOI:
https://doi.org/10.1090/S0002-9947-1991-1022865-4
MathSciNet review:
1022865
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We show that when a positive ${L_p}$ contraction is equipped with a norming function having full support, then it is related in a natural way to an operator on any other ${L_p}$ space, $1 < p < \infty$. This construction is used to generalize a theorem of Rota concerning the convergence of alternating sequences.
- M. A. Akcoglu, A pointwise ergodic theorem in $L_{p}$-spaces, Canadian J. Math. 27 (1975), no. 5, 1075â1082. MR 396901, DOI https://doi.org/10.4153/CJM-1975-112-7
- Mustafa A. Akcoglu and P. Ekkehard Kopp, Construction of dilations of positive $L_{p}$-contractions, Math. Z. 155 (1977), no. 2, 119â127. MR 448125, DOI https://doi.org/10.1007/BF01214211
- Mustafa A. Akcoglu and Louis Sucheston, On positive dilations to isometries in $L_{p}$ spaces, Measure theory (Proc. Conf., Oberwolfach, 1975) Springer, Berlin, 1976, pp. 389â401. Lecture Notes in Math., Vol. 541. MR 0451006
- M. A. Akcoglu and L. Sucheston, Pointwise convergence of alternating sequences, Canad. J. Math. 40 (1988), no. 3, 610â632. MR 960598, DOI https://doi.org/10.4153/CJM-1988-026-4
- Charn Huen Kan, On Fong and Suchestonâs mixing property of operators in a Hilbert space, Acta Sci. Math. (Szeged) 41 (1979), no. 3-4, 317â325. MR 555424 ---, Norming vectors of linear operators between ${L_p}$-spaces, Pacific J. Math. (to appear). S. Mazur, Une remarque sur lâhomĂ©omorphie des champs fonctionels, Studia Math. 1 (1929), 83-85.
- Gian-Carlo Rota, An âAlternierende Verfahrenâ for general positive operators, Bull. Amer. Math. Soc. 68 (1962), 95â102. MR 133847, DOI https://doi.org/10.1090/S0002-9904-1962-10737-X
- H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
- Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory., Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A35, 47B38, 47B60, 47B65
Retrieve articles in all journals with MSC: 47A35, 47B38, 47B60, 47B65
Additional Information
Keywords:
Positive contractions of <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L_p}$">,
alternating sequences,
maximal inequalities
Article copyright:
© Copyright 1991
American Mathematical Society