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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832549004744851456 |
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| author | Atsushi Inoue Hidekazu Ogi Mayumi Takakura |
| author_facet | Atsushi Inoue Hidekazu Ogi Mayumi Takakura |
| author_sort | Atsushi Inoue |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0f272e9241be45c0995aa9400809b424 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0f272e9241be45c0995aa9400809b4242025-02-03T06:12:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/8015280152Conditional Expectations for Unbounded Operator AlgebrasAtsushi Inoue0Hidekazu Ogi1Mayumi Takakura2Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, JapanDepartment of Functional Materials Engineering, Fukuoka Institute of Technology, Fukuoka 811-0295, JapanDepartment of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, JapanTwo 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.http://dx.doi.org/10.1155/2007/80152 |
| spellingShingle | Atsushi Inoue Hidekazu Ogi Mayumi Takakura Conditional Expectations for Unbounded Operator Algebras International Journal of Mathematics and Mathematical Sciences |
| title | Conditional Expectations for Unbounded Operator Algebras |
| title_full | Conditional Expectations for Unbounded Operator Algebras |
| title_fullStr | Conditional Expectations for Unbounded Operator Algebras |
| title_full_unstemmed | Conditional Expectations for Unbounded Operator Algebras |
| title_short | Conditional Expectations for Unbounded Operator Algebras |
| title_sort | conditional expectations for unbounded operator algebras |
| url | http://dx.doi.org/10.1155/2007/80152 |
| work_keys_str_mv | AT atsushiinoue conditionalexpectationsforunboundedoperatoralgebras AT hidekazuogi conditionalexpectationsforunboundedoperatoralgebras AT mayumitakakura conditionalexpectationsforunboundedoperatoralgebras |