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Richard V. Kadison (1925–2018)

Auteur de Fundamentals of the Theory of Operator Algebras: Elementary Theory

5 oeuvres 39 utilisateurs 2 critiques

Œuvres de Richard V. Kadison

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Autres noms
Kadison, R. V.
Date de naissance
1925-07-25
Date de décès
2018-08-22
Sexe
male
Nationalité
USA
Lieu de naissance
New York, New York, USA
Études
University of Chicago
Professions
mathematician
professor
Relations
Stone, Marshall Harvey (doctoral advisor)
James Glimm (doctoral student)
Lashof, Richard (doctoral student)
Rieffel, Marc (doctoral student)
Rørdam, Mikael (doctoral student)
Størmer, Erling (doctoral student) (tout afficher 8)
Holm, Karren M. (wife)
Kadison, Lars (son)
Organisations
University of Pennsylvania. Department of Mathmatics
Prix et distinctions
Leroy P. Steele Prize (Lifetime Achievement ∙ 1999)
National Academy of Sciences (1966)
Royal Danish Academy of Sciences and Letters (foreign member)
Norwegian Academy of Science and Letters
Guggenheim Fellowship (1969)
American Mathematical Society (2012)
Courte biographie
Richard V. Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras. Kadison was a Gustave C. Kuemmerle Professor in the Department of Mathematics of the University of Pennsylvania.

Kadison is a member of the U.S. National Academy of Sciences (elected in 1996), and a foreign member of the Royal Danish Academy of Sciences and Letters and of the Norwegian Academy of Science and Letters. He is a 1969 Guggenheim Fellow.

Kadison was awarded the 1999 Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society. In 2012 he became a fellow of the American Mathematical Society [from Wikipedia: https://en.wikipedia.org/wiki/Richard_...]

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Fundamentals of the theory of operator algebras,… par Richard V. Kadison
Indeholder "Preface", "Contents of Volume I", "Chapter 6. Comparison Theory of Projection", " 6.1 Polar decomposition and equivalence", " 6.2 Ordering", " 6.3 Finite and infinite projections", " 6.4 Abelian projections", " 6.5 Type decomposition", " 6.6 Type I algebras", " 6.7 Examples", " 6.8 Ideals", " 6.9 Exercises", "Chapter 7. Normal States and Unitary Equivalence of von Neumann Algebras", " 7.1 Completely additive states", " 7.2 Vector states and unitary implementation", " 7.3 A second approach to normal states", " 7.4 The predual", " 7.5 Normal weights on von Neumann algebras", " 7.6 Exercises", "Chapter 8. The Trace", " 8.1 Traces", " 8.2 The trace in finite algebras", " 8.3 The Dixmier approximation theorem", " 8.4 The dimension function", " 8.5 Tracial weights on factors", " 8.6 Further examples of factors", " An operator-theoretic construction", " Measure-theoretic examples", " 8.7. Exercises", "Chapter 9. Algebra and Commutant", " 9.1. The type of the commutant", " 9.2 Modular theory", " A first approach to modular theory", " Tomita's theorem - a second approach", " A further extension of modular theory", " 9.3. Unitary equivalence of type I algebras", " 9.4. Abelian von Neumann algebras", " 9.5. Spectral multiplicity", " 9.6. Exercises", "Chapter 10. Special Representation of C*-Algebras", " 10.1. The universal representation", " 10.2. Irreducible representations", " 10.3. Disjoint representations", " 10.4. Examples", " Abelian C*-algebras", " Compact operators", " B(H) and the Calkin algebra", " Uniformly matricial algebras", " 10.5. Exercises", "Chapter 11. Tensor Products", " 11.1. Tensor products of represented C*-algebras", " 11.2. Tensor products of von Neumann algebras", " Elementary properties", " The commutation theorem", " The type of tensor products", " Tensor products of unbounded operators", " 11.3. Tensor products of abstract C*-algebras", " The spatial tensor product", " C*-norms on A . B", " Nuclear C*-algebras", " 11.4 Infinite tensor products of C*-algebras", " 11.5 Exercises", "Chapter 12. Approximation by Matrix Algebras", " 12.1 Isomorphism of uniformly matricial algebras", " 12.2 The finite matricial factor", " 12.3 States and representations of matricial C*-algebras", " 12.4 Exercises", "Chapter 13. Crossed Products", " 13.1 Discrete crossed products", " 13.2 Continuous crossed products", " 13.3 Crossed products by modular automorphism groups", " 13.4 Exercises", "Chapter 14. Direct Integrals and Decompositions", " 14.1 Direct integrals", " 14.2 Decompositions relative to abelian algebras", " 14.3 Appendix - Borel mappings and analytic sets", " 14.4 Exercises", "Bibliography", "Index of Notation", "Index".

Lærebog i operatoralgebra.… (plus d'informations)
 
Signalé
bnielsen | Mar 4, 2021 |
Fundamentals of the theory of operator algebras,… par Richard V. Kadison
Indeholder "Preface", "Contents of Volume II", "Chapter 1. Linear Spaces", " 1.1 Algebraic results", " 1.2 Linear topological Spaces", " 1.3 Weak topologies", " 1.4 Extreme points", " 1.5 Normed spaces", " 1.6 Linear functionals on normed spaces", " 1.7 Some examples of Banach spaces", " 1.8 Linear operators acting on Banach spaces", " 1.9 Exercises", "Chapter 2. Basics of Hilbert Space and Linear Operators", " 2.1 Inner products on linear spaces", " 2.2 Orthogonality", " 2.3 The weak topology", " 2.4 Linear operators", " General theory", " Classes of operators", " 2.5 The lattice of projections", " 2.6 Constructions with Hilbert spaces", " Subspaces", " Direct sums", " Tensor products and the Hilbert-Schmidt class", " Matrix representations", " 2.7 Unbounded linear operators", " 2.8 Exercises", "Chapter 3. Banach Algebras", " 3.1 Basics", " 3.2 The spectrum", " The Banach algebra L1(R) and Fourier analysis", " 3.3 The Holomorphic Function Calculus", " Holomorphic functions", " The holomorphic function calculus", " 3.4 The Banach algebra C(X)", " 3.5 Exercises", "Chapter 4. Elementary C*-Algebra Theory", " 4.1 Basics", " 4.2 Order structure", " 4.3 Positive linear functionals", " 4.4 Abelian algebras", " 4.5 States and representations", " 4.6 Exercises", "Chapter 5. Elementary von Neumann Algebra Theory", " 5.1 The weak- and strong-operator topologies", " 5.2 Spectral theory for bounded operators", " 5.3 Two fundamental approximation theorems", " 5.4 Irreducible algebras - an application", " 5.5 Projection techniques and constructs", " Central carriers", " Some constructions", " Cyclicity, separation, and countable decomposability", " 5.6 Unbounded operators and abelian von Neumann Algebras", " 5.7 Exercises", "Bibliography", "Index of Notation", "Index".

Lærebog i operatoralgebra.… (plus d'informations)
 
Signalé
bnielsen | Mar 4, 2021 |
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Statistiques

Œuvres
5
Membres
39
Popularité
#376,657
Évaluation
½ 3.3
Critiques
2
ISBN
27