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

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 : E −→ E satisfies the Daugavet equation Id E +P = 1 + P . The analogous conclusion also holds for the alternative Daugavet property.

On the range of TRO-conditional expectations

“…TROs are widely studied by many authors; for instance, in [12], the authors proved that TROs form a special class of concrete operator spaces and characterized TROs in terms of the operator space theoretic properties. The interconnections between TROs and JC*-triples are studied in [3,4,5,6,7]. It is well known that an operator space is injective if and only if it is completely isometric to a ternary corner of an injective C*-algebra (see, e.g., [1]).…”