Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T15:30:32.239Z Has data issue: false hasContentIssue false
  • English
  • Français

Dilations of one Parameter Semigroups of Positive Contractions on Lp Spaces

Published online by Cambridge University Press:  20 November 2018

Gero Fendler
Gero Fendler*
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach151151 D-66041 Saarbrücken, Germany e-mail: fendler@math.uni-sb.de
Rights & Permissions [Opens in a new window]

Abstract

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.

It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an Lp-space, for 1 < p < ∞ p ≠ 2, can be dilated by a strongly continuous group of (sub)positive isometries in a manner analogous to the dilation M. A. Akçoglu and L. Sucheston constructed for a discrete semigroup of (sub)positive contractions. From this an improvement of a von Neumann type estimation, due to R. R.Coifman and G.Weiss, on the transfer map belonging to the semigroup is deduced.

Keywords

47D0322D1243A22
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 736 - 748
Copyright
Copyright © Canadian Mathematical Society 1997

References

[AS] Akçoglu, M.A. and Sucheston, L., Dilations of positive contractions on Lp-spaces. Canad. Math. Bull. 20(1977), 285–292.Google Scholar
[Bour] Bourbaki, N., Elements of Mathematics, Topological Vector Spaces, Chapters 1–5, Springer, Berlin, Heidelberg, New York, 1987.Google Scholar
[CRW] Coifman, R.R., Rochberg, R. and Weiss, G., Applications of transference: The Lp version of von Neumanns inequality and Littlewood-Paley-Stein theory. In: Linear spaces and Approximation, (eds. Butzer, P.L. and Sz, B..-Nagy), Birkhäuser, Basel 1978, 53–67.Google Scholar
[CW] Coifman, R.R. and Weiss, G., Transference methods in analysis, CBMS regional conference series in mathematics No. 31, Amer. Math. Soc., Providence, R.I., 1977.Google Scholar
[Co] Cowling, M., Harmonic analysis on semigroups. Ann. of Math. 117(1983), 267–283.Google Scholar
[DCK] Dacunha Castelle, D. and Krivine, J.-L., Applications des ultraproduits à l’étude des éspaces et des algèbres de Banach, Studia Math. XLI (1972), 315–334.Google Scholar
[Fe] Fendler, G., Herz Schur multipliers and coefficients of uniformly bounded representations, Thesis, University of Heidelberg, 1987.Google Scholar
[GdL] Glicksberg, I. and de Leeuw, K., The decomposition of certain group representations. J. Anal. Math. 15(1965), 135–192.Google Scholar
[He] Heinrich, S., Ultraproducts in Banach space theory. J. Reine Angew. Math. 313(1980), 72–104.Google Scholar
[Hz] Herz, C., Harmonic synthesis for subgroups. Ann. Inst. Fourier 23(1973), 91–123.Google Scholar
[La] Lacey, H.E., The isometric theory of classical Banach spaces, Springer, Berlin, Heidelberg, New York, 1974.Google Scholar
[Pi] Pisier, G., Completely bounded maps between sets of Banach spaces operators. Indiana Univ. Math. J. 39(1990), 251–277.Google Scholar
[SNF] Sz.-Nagy, B. and Foia¸s, C., Harmonic analysis of operators on Hilbert space, Akadémiai Kiadó, Budapest, 1970.Google Scholar