The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911769287458816 |
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| author | Cabezas, David Martín, Miguel Peralta, Antonio M. |
| author_facet | Cabezas, David Martín, Miguel Peralta, Antonio M. |
| contents | We prove that every JB$^*$-triple $E$ (in particular, every $C^*$-algebra) satisfying the Daugavet property also satisfies the stronger polynomial Daugavet property, that is, every weakly compact polynomial $P\colon E \longrightarrow E$ satisfies the Daugavet equation $\|\hbox{id}_{E} + P\| = 1+\|P\|$. The analogous conclusion also holds for the alternative Daugavet property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11621 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples Cabezas, David Martín, Miguel Peralta, Antonio M. Operator Algebras Functional Analysis We prove that every JB$^*$-triple $E$ (in particular, every $C^*$-algebra) satisfying the Daugavet property also satisfies the stronger polynomial Daugavet property, that is, every weakly compact polynomial $P\colon E \longrightarrow E$ satisfies the Daugavet equation $\|\hbox{id}_{E} + P\| = 1+\|P\|$. The analogous conclusion also holds for the alternative Daugavet property. |
| title | The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2206.11621 |