%0 Journal Article
%T Conditional Expectations for Unbounded Operator Algebras
%A Atsushi Inoue
%A Hidekazu Ogi
%A Mayumi Takakura
%J International Journal of Mathematics and Mathematical Sciences
%D 2007
%I Hindawi Publishing Corporation
%R 10.1155/2007/80152
%X 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.
%U http://www.hindawi.com/journals/ijmms/2007/080152/abs/