Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T03:48:43.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Cones arising from C*-subalgebras and complete positivity

Published online by Cambridge University Press:  01 July 2008

FLORIN POP  and
ROGER R. SMITH
FLORIN POP
Affiliation:
Department of Mathematics, and Computer Science, Wagner College, Staten Island, NY 10301U.S.A.
ROGER R. SMITH
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let B ⊆ A be an inclusion of C*-algebras. Then B is said to norm A if, for each X ∈ (A), In this paper we introduce and study the cones These are shown to coincide with the standard positive cones precisely when B norms A, and we apply this to obtain automatic complete positivity of certain positive maps between C*-algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 121 - 127
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Choi, M.-D. and Effros, E.G.. Injectivity and operator spaces. J. Funct. Anal. 24 (1977), 156–209.Google Scholar
[2]Effros, E.G. and Ruan, Z.-J.. Operator spaces. London Math. Soc. Monog. New Series, Vol. 23 (The Clarendon Press, Oxford University Press, New York, 2000).Google Scholar
[3]Kaneda, M. and Paulsen, V.. Characterizations of essential ideals as operator modules over C*-algebras. J. Operator Theory 49 (2003), 245–262.Google Scholar
[4]Paulsen, V.. Completely bounded maps and operator algebras. Cambridge Studies in Advanced Mathematics, Vol. 78. (Cambridge University Press, 2002).Google Scholar
[5]Pimsner, M. and Popa, S.. Entropy and index for subfactors. Ann. Sci. École Norm. Sup. 19 (1986), 57–106.Google Scholar
[6]Pisier, G.. Introduction to operator space theory. London Math. Soc. Lecture Note Series, Vol. 294 (Cambridge University Press, 2003).Google Scholar
[7]Pitts, D.. Norming algebras and automatic complete boundedness of isomorphisms of operator algebras. Proc. Amer. Math. Soc. 136 (2008), 1757–1768.CrossRefGoogle Scholar
[8]Pop, F.. On some norming properties of subfactors. Proc. Edinburgh Math. Soc. 48 (2005), 499–506.Google Scholar
[9]Pop, F., Sinclair, A. M. and Smith, R. R.. Norming C*-algebras by C*-subalgebras. J. Funct. Anal. 175 (2000), 168–196.Google Scholar
[10]Sinclair, A. M. and Smith, R. R.. Hochschild cohomology of von Neumann algebras. London Math. Soc. Lecture Note Series, Vol. 203 (Cambridge University Press, 1995).CrossRefGoogle Scholar
[11] A. van Daele. Continuous crossed products and type III von Neumann algebras. London Math. Soc. Lecture Note Series, Vol. 31 (Cambridge University Press, 1978).Google Scholar