The Daugavet property in symmetric operator spaces

Abstract

Under mild assumptions, the main results of this paper characterize a (real or complex) symmetric operator space affiliated with a semi-finite atomless von Neumann algebra $(\mathcal{M},\tau )$ possessing the Daugavet property as $L_1(\mathcal{M},\tau )$ or $\mathcal{M}$ (up to equivalent norms, or even proportional norms). Our results are new even for complex symmetric function spaces, which extend results of \cite{AKM12, KMMW13, AKM15} concerning the Daugavet property for real symmetric function spaces.