The Adjoint of a Semigroup of Linear OperatorsSpringer, 2006. nov. 15. - 198 oldal This monograph provides a systematic treatment of the abstract theory of adjoint semigroups. After presenting the basic elementary results, the following topics are treated in detail: The sigma (X, X )-topology, -reflexivity, the Favard class, Hille-Yosida operators, interpolation and extrapolation, weak -continuous semigroups, the codimension of X in X , adjoint semigroups and the Radon-Nikodym property, tensor products of semigroups and duality, positive semigroups and multiplication semigroups. The major part of the material is reasonably self-contained and is accessible to anyone with basic knowledge of semi- group theory and Banach space theory. Most of the results are proved in detail. The book is addressed primarily to researchers working in semigroup theory, but in view of the "Banach space theory" flavour of many of the results, it will also be of interest to Banach space geometers and operator theorists. |
Tartalomjegyzék
| 2 | |
Dichotomy theorems | 96 |
Adjoint semigroups and the | 111 |
The adjoint of a positive semigroup | 144 |
Más kiadások - Összes megtekintése
Gyakori szavak és kifejezések
adjoint semigroup arbitrary Banach lattice Banach space band preserving Bochner integrable Borel measurable bounded linear operator bounded operator Chapter closed linear closed subspace closure Co-semigroup T(t Co(IR Conversely convex Corollary denote densely defined disjoint dual space equicontinuous equivalent norm Example Fav(T(t Favard class Hahn-Banach theorem Hence Hille-Yosida operator identified implies inclusion map integrated semigroup intertwined semigroup L¹(IR L¹(R L¹(µ Lemma Let T(t linear span linear subspace multiplication semigroup O-reflexive with respect order continuous norm perturbation positive Co-semigroup positive semigroup proof of Theorem Proposition proved quasi-interior point quotient reflexive respect to T(t restriction result Riesz space Schauder basis Section semigroup dual semigroup T(t separable sequence shows strongly continuous sublattice subset Suppose T(t)-invariant To(t topology translation group trivial uniformly continuous vector weak weak*-continuous semigroup weak*-dense weakly compact X©)-compact X₁