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Elementary theory of one-parameter semigroups

Part of the Operator Theory: Advances and Applications book series (OT, volume 173)

Abstract

In the first chapter of the book, we give an introduction to the theory of one-parameter operator semigroups. We begin with the splitting theorem of Jacobs- Deleeuw-Glicksberg and the Eberlein mean ergodic theorem for a one-parameter operator semigroup. Then we present the elementary theory of C0-semigroups and discuss some relations between spectral properties of the generator of a C0- semigroup and its asymptotic behavior. We follow the standard textbooks [13], [48], [57], [67], [74], [80], [130], and send the reader for other deep and delicious topics of this theory to those books and to [17], [67], [87], [41], [89]. In the last section, we discuss the asymptotically finite-dimensional semigroups. We use frequently well-known results from operator theory and functional analysis, and send the reader to standard textbooks [2], [74], [105], and [130] for them.

Keywords

Banach Space Ergodic Theorem Equivalent Norm Elementary Theory Complex Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 2007

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