ABSTRACT
Co-SEMIGROUPS, WELL POSED EVOLUTION EQUATIONS, SPECTRAL THEORY A ND A LMOST PERIODICITY OF FUNCTIONS
1 . 1. STRONGLY CONTINUOUS SEMIGROUPS OF LINEAR OP ERATORS
In this section we collect some well-known facts from the theory of strongly contin uous semigroups of operators on a Banach space for the reader's convenience. We will focus the reader's attention on several important classes of semigroups such as analytic and compact semigroups which will be discussed later in the next chapters. Among the basic properties of strongly continuous semigroups we will put emphasis on the spectral mapping theorem. Since the materials of this section as well as of the chapter in the whole can be found in any standard book covering the area, here we aim at freshening up the reader's memory rather than giving a logically self contained account of the theory.
