Van Neerven J. — The Adjoint Of A Semigroup Of Linear Operators :: Электронная библиотека попечительского совета мехмата МГУ

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Van Neerven J. — The Adjoint Of A Semigroup Of Linear Operators

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Название: The Adjoint Of A Semigroup Of Linear Operators

Автор: Van Neerven J.

Аннотация:

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.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2008

Количество страниц: 208

Добавлена в каталог: 05.07.2008

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Предметный указатель

$\odot$ -reflexive      1.3 1.5 2.5 3.2 3.4 5.1 6.1 6.2 8.1 8.4
Adjoint semigroup      1.2
AL-space      8.3
AM-space      8.3
Approximation property      7.3
atom      8.4
Axiom K      5.5
Baire-1 functional      5.2 5.3
Banach lattice      8.1
Band      8.1
Band projection      8.1
Basis      1.5 2.1 2.3 3.2 6.2
Basis constant      1.5 2.3
Basis, boundedly complete      1.5 3.2
Basis, Schauder      see "Basis"
Basis, shrinking      1.5 3.2
Basis, summing      2.3 6.2
Basis, unconditional      1.6 8.4
Bilinear form      7.2
Bosom      1.3
Cauchy problem      4.3
Characteristic      2.6
Circled      2.3
Co-dimension      1.5 5.2 6.2
Complexification      8.4 8.6
Coordinate functional      1.5
Dedekind complete      8.1
Dedekind complete, $\sigma$ -      8.1
Disjointness      8.2
Domain      1.1
Dual, semigroup-      1.3
Dunford — Pettis property      1.5 2.5 5.2 6.2 8.4
Embedding      A1
Embedding, $G_{\delta}$ -      3.2
Embedding, natural, j      1.3 2.3
Embedding, natural, k      5.1
Embedding, semi-      3.2
Equicontinuous      2.2
Equicontinuous, weakly      2.2
Essentially separably valued      A2
Exponential formula      A3
Factorisation scheme      6.3 7.4
Favard class      3.2 3.4 4.2 4.4 6.2
Frechet space      1.6
Gagliardo completion      3.5
Generator      A3
Generator of intertwined semigroup      3.1 4.4 4.5
Generator of regular semigroup      4.4
Generator, weak*-      1.2 4.4
Graph      1.1
Grothendieck property      1.5 1.6 5.2 6.2
Group, $C_{0}$ -      A3 5.3 6.2
Growth bound      4.4 8.4
Hille — Yosida operator      3.1
Hille — Yosida operator, generalized      3.1
Hille — Yosida operator, holomorphic      3.1 3.5
Hoelder space      3.4
Ideal      8.1
Ideal, M-      2.6
Ideal, operator-      2.2 7.3
Injection      A1
Integral, Bochner      A2
Integral, Pettis      5.2 A2
Integral, Riemann weak*-      1.6 A2
Integral, weak*-      1.2 5.2 A2
Integrated semigroup      2.5 4.4
Integrated semigroup, exponentially bounded      4.4
Integrated semigroup, locally Lipschitz      4.4
Integrated semigroup, non-degenerate      4.4
Interpolation space      3.3
James function space JF      8.3
James space J      1.5 6.2
K-functional      3.3
Laplace transform      A3
Lattice isomorphism      8.1
Lebesgue number      2.2
Limes superior estimate      8.2
Mackey topology      2.6
Martin's Axiom      8.3
Measurable, Riemann      8.3
Measurable, strongly      A2 A3
Measurable, weakly      A2 5.2 8.3
Measurable, weakly Borel      A2 5.2 8.3
Modulus      8.1
Modulus of an operator      7.4 8.4
Norm, $||\cdot||^{'}$ -      1.3 2.3 3.2
Norm, cross      7.2
Norm, injective tensor      7.2
Norm, projective tensor      7.2
Norming      A2
Null set, E-      8.4
Operator, adjoint      1.1
Operator, band preserving      8.4
Operator, closed      1.1
Operator, cone absolutely summing      7.4
Operator, densely defined      1.1
Operator, integral      7.3
Operator, l-nuclear      7.4
Operator, nuclear      7.3
Operator, positive      8.1
Operator, r-compact      7.4

Operator, representable      6.2 7.3
Operator, weakly compact      A1 2.5 6.3
Order bounded set      8.1
Order continuous norm      1.6 8.1 8.2 8.3 8.4
Order interval      8.1
Order unit      8.3
Order unit, weak      8.4
Part of an operator      1.3
Perturbation      4.1 4.2
Pettis Integral Property (PIP)      5.5
polar      2.3
Projection band      8.1
Quasi-complete      2.6
Quasi-interior point      8.2 8.6
Quasi-reflexive      2.5 6.2 6.3
Radon — Nikodym Property (RNP)      1.6 3.1 6.2 7.4
Reflexive      A1 1.3 1.5 3.1 3.2 8.4
Representation space      8.4
Resolvent      1.4
Resolvent identity      1.4
Resolvent set      1.4
Riesz space      8.1
Riesz space homomorphism      8.1
Riesz space isomorphism      8.1
Riesz subspace      8.1
Schauder basis      see "Basis"
Schauder decomposition      1.6
Semigroup, $C_{0}$       A3
Semigroup, $C_{>0}$       A3 3.1 5.3 6.2
Semigroup, adjoint      1.2
Semigroup, compact      5.2
Semigroup, contraction      A3
Semigroup, convolution      6.2
Semigroup, holomorphic      5.2
Semigroup, intertwined      3.1 4.1 4.4
Semigroup, lattice      8.1
Semigroup, locally bounded      A3
Semigroup, multiplication      8.4 8.5
Semigroup, one-parameter      A3
Semigroup, Pettis integrable      5.2
Semigroup, positive      8.1
Semigroup, quotient      2.5 5.2
Semigroup, regular      4.4
Semigroup, rotation      1.3
Semigroup, strongly continuous      A3
Semigroup, strongly measurable      A3 5.3 6.2
Semigroup, summing      2.3 6.2
Semigroup, translation      1.3 2.2 5.2 6.1 7.1 7.3 7.4 8.2 8.3
Semigroup, uniformly continuous      A3 1.3 3.2 6.2
Semigroup, weak*-continuous      A3 1.6 4.4 6.2
Semigroup, weakly Borel measurable      5.2 8.3
Semigroup, weakly compact      5.2 6.2 8.4
Semigroup, weakly continuous      A3
Solid hull      8.1
Solution, classical      4.3
Solution, mild      4.3
Spectrum      1.4
Stone — Cech compactification      8.4
Stonean      8.4
Subcouple      3.3
Subcouple, exact      3.3
Sublattice      8.1
Sun      1.3
Tensor product, algebraic      7.2
Tensor product, injective      7.2
Tensor product, l-      7.4
Tensor product, projective      7.2
Theorem, Banach — Alaoglu      A1
Theorem, bipolar      6.1
Theorem, Bochner      A2
Theorem, closed graph      A1
Theorem, dichotomy      5.3
Theorem, Eberlein — Shmulyan      A1 2.2
Theorem, Gantmacher      A1
Theorem, Goldstine      A1
Theorem, Grothendieck      7.3
Theorem, Hahn — Banach      A1 6.1
Theorem, Hille — Yosida      A3
Theorem, Kakutani      7.3 8.3
Theorem, Kakutani — Krein      5.2 8.3
Theorem, Lotz      1.5 1.6 6.2 8.6
Theorem, measurable semigroup      A3 5.3 6.2
Theorem, Odell — Rosenthal      5.2 8.3
Theorem, open mapping      A1
Theorem, Pettis measurability      A2 5.3 7.1
Theorem, Riddle — Saab — Uhl      5.2 5.4 8.3
Theorem, Sobczyk      6.2 6.3
Theorem, uniform boundedness      A1
Theorem, weak semigroup      A3 1.5 5.2
Theorem, Wiener — Young      8.2
Theorem, Zippin      1.5 3.2
Three space problem      5.5 6.1
Topology, $\beta(X, X^{*})$       1.6
Topology, $\sigma(X, X^{\cdot})$ -      2.1
Topology, $\tau(X, X^{*})$       2.6
Topology, weak      A1
Topology, weak*-      A1
Universally measurable      5.2
Variation      7.1
Vector lattice      8.1
Weakly Compactly Generated (WCG)      1.6 2.5 6.3
ZFC      5.5

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