Inoue, Atsushi; Takakura, M.; Ogi, H. 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]. Reviewer: Khristo N. Boyadzhiev (Ada) Cited in 3 Documents MSC: 47L60 Algebras of unbounded operators; partial algebras of operators 46K10 Representations of topological algebras with involution Keywords:\(C^*\)-algebra; generalized von Neumann algebra; vector conditional expectation PDFBibTeX XMLCite \textit{A. Inoue} et al., Contemp. Math. 427, 225--234 (2007; Zbl 1134.47055)