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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Hindawi Limited
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171278000241 |
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doaj-02f152b3bb4e4af29563233c6538dbc0 |
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Article |
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doaj-02f152b3bb4e4af29563233c6538dbc02020-11-25T00:17:30ZengHindawi LimitedInternational 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. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Richard I. Loebl |
| 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. |
| author_facet |
Richard I. Loebl |
| author_sort |
Richard I. Loebl |
| title |
On the range of completely bounded maps |
| title_short |
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_sort |
on the range of completely bounded maps |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1978-01-01 |
| 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. |
| 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 |
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