Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules
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arXiv
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| Format: | Preprint |
| Published: |
2006
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| _version_ | 1866910920778711040 |
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| author | Frank, Michael |
| author_facet | Frank, Michael |
| contents | B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-algebras which characterize precisely the C*-algebras of compact operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0611348 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules Frank, Michael Operator Algebras Functional Analysis 46L08, 46H25 B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-algebras which characterize precisely the C*-algebras of compact operators. |
| title | Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules |
| topic | Operator Algebras Functional Analysis 46L08, 46H25 |
| url | https://arxiv.org/abs/math/0611348 |