On Banach space projective tensor product of $C^*$-algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Acceso en línea: | |
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| _version_ | 1866911345191944192 |
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| author | Gupta, Ved Prakash Jain, Ranjana |
| author_facet | Gupta, Ved Prakash Jain, Ranjana |
| contents | We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of $C^*$-algebras. Highlights of this analysis include (a) injectivity of the Banach space projective tensor product when restricted to the tensor products of $C^*$-algebras, (b) detailed structure of closed ideals of $A \otimes_γ B$ in terms of those of $A$ and $B$, (c) identification of certain spaces of ideals of $A \otimes_γ B$ in terms of those of $A$ and $B$ from the perspective of hull-kernel topology, and (d) identification of the center of $A \otimes_γ B$ with $Z(A) \otimes_γ Z(B)$, where $A$ and $B$ are $C^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_01131 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On Banach space projective tensor product of $C^*$-algebras Gupta, Ved Prakash Jain, Ranjana Operator Algebras Functional Analysis 46L06, 46M05, 46H10 We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of $C^*$-algebras. Highlights of this analysis include (a) injectivity of the Banach space projective tensor product when restricted to the tensor products of $C^*$-algebras, (b) detailed structure of closed ideals of $A \otimes_γ B$ in terms of those of $A$ and $B$, (c) identification of certain spaces of ideals of $A \otimes_γ B$ in terms of those of $A$ and $B$ from the perspective of hull-kernel topology, and (d) identification of the center of $A \otimes_γ B$ with $Z(A) \otimes_γ Z(B)$, where $A$ and $B$ are $C^*$-algebras. |
| title | On Banach space projective tensor product of $C^*$-algebras |
| topic | Operator Algebras Functional Analysis 46L06, 46M05, 46H10 |
| url | https://arxiv.org/abs/1809.01131 |