On Minimal Norms on Mn
We show that for each minimal norm N(⋅) on the algebra ℳn of all n×n complex matrices, there exist norms ‖⋅‖1 and ‖⋅‖2 on ℂn such that N(A)=max{‖Ax‖2:‖x‖1=1, x∈ℂn} for all A∈ℳn. This may be regarded as an extension of a known result on characterization of minimal algebra norms....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/52840 |
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| _version_ | 1832562035774193664 |
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| author | Madjid Mirzavaziri Mohammad Sal Moslehian |
| author_facet | Madjid Mirzavaziri Mohammad Sal Moslehian |
| author_sort | Madjid Mirzavaziri |
| collection | DOAJ |
| description | We show that for each minimal norm N(⋅) on the
algebra ℳn of all n×n complex matrices, there exist
norms ‖⋅‖1 and ‖⋅‖2 on ℂn such that N(A)=max{‖Ax‖2:‖x‖1=1, x∈ℂn} for all A∈ℳn. This may be regarded as an extension of a known result on characterization of minimal algebra norms. |
| format | Article |
| id | doaj-art-1f00d5f780c74da792e894ca7b00d800 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1f00d5f780c74da792e894ca7b00d8002025-02-03T01:23:30ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/5284052840On Minimal Norms on MnMadjid Mirzavaziri0Mohammad Sal Moslehian1Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, IranDepartment of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, IranWe show that for each minimal norm N(⋅) on the algebra ℳn of all n×n complex matrices, there exist norms ‖⋅‖1 and ‖⋅‖2 on ℂn such that N(A)=max{‖Ax‖2:‖x‖1=1, x∈ℂn} for all A∈ℳn. This may be regarded as an extension of a known result on characterization of minimal algebra norms.http://dx.doi.org/10.1155/2007/52840 |
| spellingShingle | Madjid Mirzavaziri Mohammad Sal Moslehian On Minimal Norms on Mn Abstract and Applied Analysis |
| title | On Minimal Norms on Mn |
| title_full | On Minimal Norms on Mn |
| title_fullStr | On Minimal Norms on Mn |
| title_full_unstemmed | On Minimal Norms on Mn |
| title_short | On Minimal Norms on Mn |
| title_sort | on minimal norms on mn |
| url | http://dx.doi.org/10.1155/2007/52840 |
| work_keys_str_mv | AT madjidmirzavaziri onminimalnormsonmn AT mohammadsalmoslehian onminimalnormsonmn |