Invertibility-preserving maps of C∗-algebras with real rank zero
In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras and Φ:A→B is a linear map onto B tha...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.685 |
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| _version_ | 1832561200847650816 |
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| author | Istvan Kovacs |
| author_facet | Istvan Kovacs |
| author_sort | Istvan Kovacs |
| collection | DOAJ |
| description | In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras and Φ:A→B is a linear map onto B that preserves the spectrum of elements, then Φ is a Jordan isomorphism if either A or B is a C∗-algebra of real rank zero. We also generalize a theorem of Russo. |
| format | Article |
| id | doaj-art-166422af62384e95b02614f477db8f75 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-166422af62384e95b02614f477db8f752025-02-03T01:25:37ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005668568910.1155/AAA.2005.685Invertibility-preserving maps of C∗-algebras with real rank zeroIstvan Kovacs0Department of Mathematics, Case Western Reserve University, Cleveland 44106, OH, USAIn 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras and Φ:A→B is a linear map onto B that preserves the spectrum of elements, then Φ is a Jordan isomorphism if either A or B is a C∗-algebra of real rank zero. We also generalize a theorem of Russo.http://dx.doi.org/10.1155/AAA.2005.685 |
| spellingShingle | Istvan Kovacs Invertibility-preserving maps of C∗-algebras with real rank zero Abstract and Applied Analysis |
| title | Invertibility-preserving maps of C∗-algebras with real rank zero |
| title_full | Invertibility-preserving maps of C∗-algebras with real rank zero |
| title_fullStr | Invertibility-preserving maps of C∗-algebras with real rank zero |
| title_full_unstemmed | Invertibility-preserving maps of C∗-algebras with real rank zero |
| title_short | Invertibility-preserving maps of C∗-algebras with real rank zero |
| title_sort | invertibility preserving maps of c∗ algebras with real rank zero |
| url | http://dx.doi.org/10.1155/AAA.2005.685 |
| work_keys_str_mv | AT istvankovacs invertibilitypreservingmapsofcalgebraswithrealrankzero |