期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2007
卷号：2007
DOI：10.1155/2007/80152
出版社：Hindawi Publishing Corporation
摘要：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.
