Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T14:24:08.318Z Has data issue: false hasContentIssue false
  • English
  • Français

Inclusions of ternary rings of operators and conditional expectations

Published online by Cambridge University Press:  28 June 2013

PEKKA SALMI  and
ADAM SKALSKI
PEKKA SALMI
Affiliation:
Department of Mathematical Sciences, University of Oulu PL 3000, FI-90014 Oulun yliopisto, Finland. e-mail: [email protected]
ADAM SKALSKI
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences ul.Śniadeckich 8, 00-956 Warszawa, Poland. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P: T → X then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 475 - 482
Copyright
Copyright © Cambridge Philosophical Society 2013 

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

[Con00]Conway, J. B.A Course in Operator Theory (American Mathematical Society, 2000).Google Scholar
[EOR01]Effros, E. G., Ozawa, N. and Ruan, Z.–J.On injectivity and nuclearity for operator spaces. Duke Math. J. 110 (2001), 489–521.CrossRefGoogle Scholar
[Ham99]Hamana, M.Triple envelopes and Šilov boundaries of operator spaces. Math. J. Toyama Univ. 22 (1999), 77–93.Google Scholar
[KaRu02]Kaur, M. and Ruan, Z–J.Local properties of ternary rings of operators and their linking C*-algebras. J. Funct. Anal. 195 (2002), 262–305.CrossRefGoogle Scholar
[NeRu02]Neal, M. and Russo, B.Operator space characterizations of C*-algebras and ternary rings. Pacific J. Math. 209 (2003), 339–364.CrossRefGoogle Scholar
[NSSS12]Neufang, M., Salmi, P., Skalski, A. and Spronk, N. Contractive idempotents on locally compact quantum groups. To appear in Indiana Univ. Math. J., available at arXiv:1209.6508.Google Scholar
[You83]Youngson, M. A.Completely contractive projections on C*-algebras. Quart. J. Math. Oxford Ser. (2) 34 (1983), 507–511.CrossRefGoogle Scholar