Multiplication operators in some classes of (LF) and (PLB)-sequence spaces

Abstract

The main aim of this paper is to investigate multiplication operators acting in some inductive limits of Fréchet sequence spaces and in some projective limits of (LB)-sequence spaces introduced and studied by the authors in a previous work. More precisely, we determine the continuity, boundedness, and compactness of these operators as well as their spectra. We also analyze their ergodic properties, that is, power boundedness, (uniform) mean ergodicity, and supercyclicity. Finally, we characterize the continuity and boundedness of related operators defined in these spaces.