Spectra and dynamics of generalized Cesàro operators in (LF) and (PLB) sequence spaces

In this paper, we introduce inductive limits of the Fr & eacute;chet spaces l (p+), ces(p+),andd(p+)(1 <= p<infinity) and projective limits of the (LB)-spaces l(p-), ces(p-),andd(p-)(1<p <=infinity). After having established some topological properties ofsuch spaces as acyclicity and ultrabornologicity, we prove that the generalized Ces & agrave;rooperatorsC(t)(0 <= t <= 1) act continuously in these sequence spaces, and we determinethe spectra. Finally, we study the ergodic properties, that is, power boundedness,(uniform) mean ergodicity, and supercyclicity, of the operatorsCtacting in the (LF)-spaces and in the (PLB)-spaces mentioned above