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Unbounded conditional expectations for $$O^*$$-algebras. (English) Zbl 1134.47055
Mallios, Anastasios (ed.) et al., Topological algebras and their applications. Proceedings of the 5th international conference, Athens, Greece, June 27–July 1, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-3868-6/pbk). Contemporary Mathematics 427, 225-234 (2007).
The authors define and investigate unbounded conditional expectations (UCE) of $$O^*$$-algebras. It is proved that there exists a largest UCE. A necessary and sufficient condition is provided for the existence of conditional expectations in terms of Tomita’s modular theory.
For the entire collection see [Zbl 1109.46003].

##### MSC:
 47L60 Algebras of unbounded operators; partial algebras of operators 46K10 Representations of topological algebras with involution