The Daugavet equation for polynomials on C${}^{\ast }$-algebras and JB${}^{\ast }$-triples

Abstract

We prove that every JB${}^{\ast }$-triple $E$ (in particular, every $C^{\ast }$-algebra) satisfying the Daugavet property also satisfies the stronger polynomial Daugavet property, that is, every weakly compact polynomial $P:E⟶E$ satisfies the Daugavet equation $\Vert {id}_E+P\Vert =1+\Vert P\Vert$. The analogous conclusion also holds for the alternative Daugavet property.

References in corpus (2)

• Extension of isometries from the unit sphere of a rank-2 Cartan factor
• Grothendieck's inequalities for JB${}^{\ast }$-triples: Proof of the Barton-Friedman conjecture