$m$-accretive operators with $m$-dispersive resolvents

Abstract:

We characterize linear $m$-accretive operators with $m$-dispersive resolvents. $T$ is linear and $m$-accretive, with ${(\lambda + T)^{ - 1}}$ $m$-dispersive, if and only if the sequence $\left \langle {n!\phi {{(\lambda + T)}^{n + 1}}x} \right \rangle _{n = 0}^\infty$ equals the moments of a positive measure on the positive real line, for sufficiently many $\phi$ in ${X^*}$, $x$ in $X$.