Conditional Expectations for Unbounded Operator Algebras
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 b...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/80152 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |