Abstract
Given a family of completely positive maps, indexed by a group, from aC*-algebra into itself, we are concerned with its dilation to a group of *-automorphisms on a larger algebra. A Schwarz-type inequality forn-positive *-linear mappings from an involutive algebra into the bounded linear operators on a hilbert space is obtained. Strongly continuous one-parameter semigroups and groups onC*-algebras, which have certain positivity properties, are studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ando, T.: Acta Sci. Math. (Szeged)24, 88–90 (1963)
Araki, H.: Publ. Res. Inst. Math. Sci., Kyoto Univ.8, 439–469 (1972–73)
Arveson, W. B.: Acta Math.123, 141–224 (1969)
Davies, E. B.: Z. Wahrscheinlichkeitstheorie verw. Geb.23, 261–273 (1972)
Davies, E. B.: Commun. math. Phys.39, 91–110 (1974)
Evans, D. E.: Thesis, Oxford (1975)
Lieb, E. H., Ruskai, M. B.: Advan. Math.12, 269–273 (1974).
Lindblad, G.: Commun. math. Phys.40, 147–151 (1975)
Lindblad, G.: On the generators of quantum dynamical semigroups, Preprint, Royal Institute of Technology, Stockholm (1975)
Stinespring, W. F.: Proc. Amer. Math. Soc.6, 211–216 (1955)
Stroescu, E.: Pacific J. Math.47, 257–267 (1973)
Sz.-Nagy, B., Foias, C.: Harmonic analysis of operators on hilbert space. Amsterdam: North Holland Publ. Co. 1970
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki
Rights and permissions
About this article
Cite this article
Evans, D.E. Positive linear maps on operator algebras. Commun.Math. Phys. 48, 15–22 (1976). https://doi.org/10.1007/BF01609408
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01609408