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arXiv · 2206.11621

The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples

David Cabezas·Miguel Martín·Antonio M. Peralta
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Abstract

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.

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David Cabezas, Miguel Martín, Antonio M. Peralta. 2022-06-23. The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples. https://doi.org/10.1016/j.aim.2023.109479

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