The Daugavetian index of a Banach space (Q1428963)

The author defines the Daugavetian index \(\text{daug}\;X\) of a Banach space as the biggest constant \(m\) such that \(\| \text{ Id}+T\| \geq 1+m\| T\| \) for all compact operators on~\(X\). The case \(m=1\) is equivalent to the Daugavet property of \(X\) introduced by \textit{V.~Kadets, R.~V. Shvidkoy, G.~G. Sirotkin} and \textit{D.~Werner} [Trans. Am. Math. Soc. 352, 855--873 (2000; Zbl 0938.46016)]. Here, the Daugavetian index is characterised in terms of numerical ranges, and some stability properties are proved; e.g., \(\text{daug}\;C(K,X)\) is the maximum of \(\text{daug}\;C(K)\) and \(\text{daug}\;X\).