One-parameter Semigroups of Positive Operators
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Beschreibung
This volume develops the structural theory of one‑parameter semigroups of positive operators on ordered Banach spaces, addressing the fundamental problem of characterizing their generators, spectral properties, and asymptotic behavior. Such semigroups form a central analytical framework for models arising in partial differential equations, probability theory, ergodic theory, and mathematical physics.
Since its first publication in 1986, the book has become a foundational reference, offering a rigorous and unified treatment of positivity, Banach lattices, and semigroup theory. The exposition covers Banach spaces, Banach lattices, C(X) spaces, and operator algebras, with a systematic focus on generator theory, spectral analysis, and long‑time behavior.
This second edition preserves the original conceptual framework and organization while presenting the entire text in a fully revised and professionally typeset form. Misprints have been corrected, references updated, and a new chapter of notes surveys key developments of the past four decades, placing the original results in a modern context without compromising their historical coherence. The book remains an essential resource for researchers and advanced graduate students in operator theory and functional analysis.
This volume develops the structural theory of one‑parameter semigroups of positive operators on ordered Banach spaces, addressing the fundamental problem of characterizing their generators, spectral properties, and asymptotic behavior. Such semigroups form a central analytical framework for models arising in partial differential equations, probability theory, ergodic theory, and mathematical physics.
Since its first publication in 1986, the book has become a foundational reference, offering a rigorous and unified treatment of positivity, Banach lattices, and semigroup theory. The exposition covers Banach spaces, Banach lattices, C(X) spaces, and operator algebras, with a systematic focus on generator theory, spectral analysis, and long‑time behavior.
This second edition preserves the original conceptual framework and organization while presenting the entire text in a fully revised and professionally typeset form. Misprints have been corrected, references updated, and a new chapter of notes surveys key developments of the past four decades, placing the original results in a modern context without compromising their historical coherence. The book remains an essential resource for researchers and advanced graduate students in operator theory and functional analysis.
A classical foundational text on positive operator semigroups, now fully updated and typeset in TeX Presents a rigorous and unified treatment of positivity, Banach lattices, and one-parameter semigroup theory Provides numerous structural functional analytic results that remain essential in modern analysis and applications
Autor*in
Wolfgang Arendt
Themen in »One-parameter Semigroups of Positive Operators«
Operator Semigroups Positive Operators Banach Lattices Spectral Theory Operator Algebras Partial Differential Equations