Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-31T16:01:15.479Z 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, Postfach 151151 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

Information

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