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Conditional Expectations for Unbounded Operator Algebras

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  • Atsushi Inoue
  • Hidekazu Ogi
  • Mayumi Takakura

Abstract

Two conditional expectations in unbounded operator algebras ( O ∗ -algebras) are discussed. One is a vector conditional expectation defined by a linear map of an O ∗ -algebra into the Hilbert space on which the O ∗ -algebra acts. This has the usual properties of conditional expectations. This was defined by Gudder and Hudson. Another is an unbounded conditional expectation which is a positive linear map ℰ of an O ∗ -algebra ℳ onto a given O ∗ -subalgebra 𝒩 of ℳ . Here the domain D ( ℰ ) of ℰ does not equal to ℳ in general, and so such a conditional expectation is called unbounded.

Suggested Citation

  • Atsushi Inoue & Hidekazu Ogi & Mayumi Takakura, 2007. "Conditional Expectations for Unbounded Operator Algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-22, June.
    • Handle: RePEc:hin:jijmms:080152
    DOI: 10.1155/2007/80152
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