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Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups

Part of the Operator Theory: Advances and Applications Book Series (volume 173)

DOI: 10.1007/978-3-7643-8114-1

ISBN: 978-3-7643-8095-3

Publisher: Birkhäuser Basel - Springer Journals

Jan 1, 2007

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Chapter 1Elementary theory of one-parameter semigroups

Pages: 1 –64

[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...
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Chapter 2Positive semigroups in ordered Banach spaces

Pages: 65 –115

[In this chapter, we deal with one-parameter positive semigroups in ordered Banach spaces. Firstly, we discuss the notion of ideally ordered Banach spaces and uniformly order convex Banach spaces. Both classes include Lp-spaces (1 ≤ p < ∞) as well as preduals of von Neumann algebras. We prove...
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Chapter 3Positive semigroups in L1-spaces

Pages: 117 –158

[In this chapter, we investigate asymptotic properties of one-parameter positive semigroups in L1(Ω, Σ, μ), where (Ω, Σ, μ) is a measure space with a σ-finite measure μ. In the last section, we shall also consider the theory of Markov semigroups in so-called non-commutative L1-spaces. For...

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