The Cesàro operator on duals of power series spaces of infinite type

2018/02/13 by Albanese, Angela A., Bonet, José, Ricker, Werner J.
#46A11 #46A13 #46A45 #47A35 #47B37 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A10 #Secondary 46A04

paper · doi:10.48550/arxiv.1802.04569

Abstract

A detailed investigation is made of the continuity, spectrum and mean ergodic properties of the Cesàro operator C when acting on the strong duals of power series spaces of infinite type. There is a dramatic difference in the nature of the spectrum of C depending on whether or not the strong dual space (which is always Schwartz) is nuclear.

Related

• The Cesàro operator on power series spaces
• Generalized Cesàro operators in the disc algebra and in Hardy spaces
• Mean ergodic properties of the continuous Cesàro operators
• Cesàro operators on the space of analytic functions with logarithmic growth
• Spectral and ergodic properties of the operator B(r,s) over power series spaces Λ_∞(α) of infinite type and their duals