English

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

Operator Algebras 2024-02-05 v1 Functional Analysis

Abstract

We prove that every JB^*-triple EE (in particular, every CC^*-algebra) satisfying the Daugavet property also satisfies the stronger polynomial Daugavet property, that is, every weakly compact polynomial P ⁣:EEP\colon E \longrightarrow E satisfies the Daugavet equation idE+P=1+P\|\hbox{id}_{E} + P\| = 1+\|P\|. The analogous conclusion also holds for the alternative Daugavet property.

Keywords

Cite

@article{arxiv.2206.11621,
  title  = {The Daugavet equation for polynomials on C$^*$-algebras and JB$^*$-triples},
  author = {David Cabezas and Miguel Martín and Antonio M. Peralta},
  journal= {arXiv preprint arXiv:2206.11621},
  year   = {2024}
}