On the range of completely bounded maps
It is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅𝒞⊗Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices.
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| Format: | Article |
| Language: | English |
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Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000241 |
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| _version_ | 1832549350108037120 |
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| author | Richard I. Loebl |
| author_facet | Richard I. Loebl |
| author_sort | Richard I. Loebl |
| collection | DOAJ |
| description | It is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅𝒞⊗Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices. |
| format | Article |
| id | doaj-art-02f152b3bb4e4af29563233c6538dbc0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-02f152b3bb4e4af29563233c6538dbc02025-02-03T06:11:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011220921510.1155/S0161171278000241On the range of completely bounded mapsRichard I. Loebl0Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USAIt is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅𝒞⊗Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices.http://dx.doi.org/10.1155/S0161171278000241completely bounded mapsC*-algebrasvon Neumann algebrasextension of maps. |
| spellingShingle | Richard I. Loebl On the range of completely bounded maps International Journal of Mathematics and Mathematical Sciences completely bounded maps C*-algebras von Neumann algebras extension of maps. |
| title | On the range of completely bounded maps |
| title_full | On the range of completely bounded maps |
| title_fullStr | On the range of completely bounded maps |
| title_full_unstemmed | On the range of completely bounded maps |
| title_short | On the range of completely bounded maps |
| title_sort | on the range of completely bounded maps |
| topic | completely bounded maps C*-algebras von Neumann algebras extension of maps. |
| url | http://dx.doi.org/10.1155/S0161171278000241 |
| work_keys_str_mv | AT richardiloebl ontherangeofcompletelyboundedmaps |