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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: pekka.salmi@iki.fi
ADAM SKALSKI
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences ul.Śniadeckich 8, 00-956 Warszawa, Poland. e-mail: a.skalski@impan.pl
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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 

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References

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