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On Induced Operators

Published online by Cambridge University Press:  20 November 2018

R. E. Bradley
R. E. Bradley*
Affiliation:
Department of Mathematics Northwestern University Evanston, Illinois 60208, USA
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Abstract

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We show that when a positive contraction of type (p, q) is equipped with a positive norming function having full support, then it is related in a natural way to operators on other Lp spaces.

Keywords

28D9947A35Positive contractions of Lpnorming functionsalternating sequences
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 477 - 494
Copyright
Copyright © Canadian Mathematical Society 1991

References

[Al Akcoglu, M.A., A pointwise ergodic theorem in Lp-spaces, Can. J. Math. 27(1975), 1075–1082.Google Scholar
[AB1 Akcoglu, M.A. and Bradley, R.E., Alternating sequences and induced operators, Trans. AMS, to appear.Google Scholar
[AS1] Akcoglu, M.A. and Sucheston, L., On positive dilations to isometries in Lp spaces, in Measure Theory Oberwohlfach 1975, Springer-Verlag Lecture Notes 541, New York, 1976.Google Scholar
[AS2] Akcoglu, M.A. and Sucheston, L., Dilations of positive contractions on Lp spaces, Canad. Math. Bull. 20(1977), 285–292.Google Scholar
[AS3] Akcoglu, M.A. and Sucheston, L., An alternating procedure for operators on Lp spaces, Proc. AMS 99(1987), 555–558.Google Scholar
[AS4] Akcoglu, M.A. and Sucheston, L., Pointwise convergence of alternating sequences, Can. J. Math. 40(1988), 610–632.Google Scholar
[B] Bradley, R.E., Induced operators and alternating sequences. Thesis, University of Toronto, Toronto, 1989.Google Scholar
[BC] Burkholder, D.L. and Chow, Y.S., Iterates of conditional expectation operators, Proc. AMS 12(1961), 490–495.Google Scholar
[D] Doob, J.L., A ratio operator limit theorem, Z. Wahrsch. 1(1963), 288–294.Google Scholar
[E] Edwards, R.E., Fourier Series, vol 2. 2nd éd., Springer-Verlag Graduate Texts 85, New York, 1982.Google Scholar
[I] Ionescu-Tulcea, A., Ergodic properties of isometries in Lp-spaces, Bull. AMS 70(1964), 366–371.Google Scholar
[Kl] Kan, C.H., On Fong and Sucheston's property ofoperators in a Hilbert space, Acta Sci. Math. 41(1979), 317–325.Google Scholar
[K2] Kan, C.H., A class of extreme Lp contractions, p1,2, ∞, and real 2 x 2 matrices, Illinois J. Math. 30(1986), 612–635.Google Scholar
[R] Rota, G.C., An “Alternie rende Verfahren” for general positive operators, Bull. AMS 68(1962), 95–102.Google Scholar
[Ro] Roy, H.L. den, Real Analysis. Macmillan, New York, 1968.Google Scholar
[S] Starr, N., Operator limit theorems, Trans. AMS, 121(1966), 90–115.Google Scholar
[St] Stein, E.M., On the maximal ergodic theorem, Proc. Nat. Acad. Sci. USA 47(1961), 1894–1897.Google Scholar