Kernel sections for processes and nonautonomous lattice systems

Abstract

In this paper, we first establish a set of sufficient and necessaryconditions for the existence of globally attractive kernel sectionsfor processes defined on a general Banach space and a weighted spaceℓ$_\rho ^p$ of infinite sequences ($p\geq 1)$, respectively.Then we obtain an upper bound of the Kolmogorov$\varepsilon$-entropy of kernel sections for processes on theHilbert space ℓ$_\rho ^2 $. As applications, we investigatecompact kernel sections for first order, partly dissipative, andsecond order nonautonomous lattice systems on weighted spacescontaining bounded sequences.