The Adjoint of a Semigroup of Linear Operators
Springer Berlin Heidelberg, 1992. dec. 14. - 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.
Mit mondanak mások - Írjon ismertetőt
Nem találtunk ismertetőket a szokott helyeken.
The adjoint semigroup
The crX Xtopology
Interpolation extrapolation and duality
8 további fejezet nem látható
Más kiadások - Összes megtekintése
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 cr(X D(Ah denote densely defined disjoint dual space equicontinuous equivalent norm Example Fav(T(t Favard class finite rank operators Hahn-Banach theorem Hence Hille-Yosida operator identified implies inclusion map integrated semigroup intertwined semigroup Lemma Let T(t linear span linear subspace multiplication semigroup order continuous norm positive Co-semigroup positive semigroup proof of Theorem Proposition proved quasi-interior point quotient reflexive with respect respect to T(t restriction result Riesz space Schauder basis Section semigroup dual semigroup T(t separable sequence shows strongly continuous sublattice subset Suppose TB(t Theorem A3.1 To(t topology translation group trivial Tx(t uniformly continuous vector weak weak*-continuous semigroup weak*-dense weak*-integral weakly Borel measurable weakly compact X0)-compact X0)-topology XR(X