Inclusions of ternary rings of operators and conditional expectations

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.

7 pages, v2/3 introduces a few minor changes. The paper will appear in the Mathematical Proceedings of the Cambridge Philosophical Society