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Unbounded conditional expectations for partial \(O^{\ast}\)-algebras. (English) Zbl 1173.47054

In this paper, the author discusses a particular class of maps, the so-called conditional expectations defined on partial O*-algebras, and some possible generalizations.
Specifically, the author extends to partial O*-algebras some definitions and results originally given, together with other authors, for O*-algebras. After a section of preliminaries, the author introduces the notion of weak and unbounded conditional expectations and find, among other results, necessary and sufficient conditions for the existence of a conditional expectation on a selfadjoint partial O*-algebra.

MSC:

47L60 Algebras of unbounded operators; partial algebras of operators
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References:

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[3] A. Inoue, M. Takakura, and H. Ogi, “Unbounded conditional expectations for O\ast -algebras,” Contemporary Mathematics, vol. 427, pp. 225-234, 2007. · Zbl 1134.47055
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