Pseudo-resolvents

The present paper is divided into two sections. In the first section we recall the notions of resolvent and pseudo-resolvent, and a, few remarkable properties. In the second section we introduce a new concept, the L-infinity-type pseudo-resolvent, and prove a characterization theorem. The generators of L-infinity-type pseudo-resolvents are characterized in spectral terms. The connection between the L-infinity-type pseudo-resolvents and C-o-equicontinuous semigroups is pointed out.