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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2001
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/math/0106131 |
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| _version_ | 1866916725117681664 |
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| author | Frank, Michael Paulsen, Vern I. |
| author_facet | Frank, Michael Paulsen, Vern I. |
| contents | In this paper we give some characterizations of M. Hamana's injective envelope I(A) of a C*-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C*-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yields a natural representation of many kinds of multipliers as multiplications by elements of I(A). In particular, we prove that the(n times iterated) local multiplier algebra of A embeds into I(A). Some remarks on local left/right/quasi multiplier algebras as subsets of I(A) are added. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0106131 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Injective Envelopes of $C^*$-algebras as Operator Modules Frank, Michael Paulsen, Vern I. Operator Algebras Functional Analysis 46L08, 46L01 In this paper we give some characterizations of M. Hamana's injective envelope I(A) of a C*-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C*-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yields a natural representation of many kinds of multipliers as multiplications by elements of I(A). In particular, we prove that the(n times iterated) local multiplier algebra of A embeds into I(A). Some remarks on local left/right/quasi multiplier algebras as subsets of I(A) are added. |
| title | Injective Envelopes of $C^*$-algebras as Operator Modules |
| topic | Operator Algebras Functional Analysis 46L08, 46L01 |
| url | https://arxiv.org/abs/math/0106131 |