Fundamentals of the theory of operator algebras. Volume I, Elementary theory / Richard V. Kadison, John R. Ringrose.

Format:

Book

Author/Creator:

Kadison, Richard V., 1925- author.

Ringrose, John R., author.

Series:

Graduate studies in mathematics ; v. 15.

Graduate studies in mathematics ; volume 15

Language:

English

Subjects (All):

Operator algebras.

Physical Description:

1 online resource (398 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1997]

Language Note:

English

Summary:

The first volume of a two-volume text for an intermediate graduate course or for self-study for students familiar with basic measure theory and topology. Volume one covers linear spaces, Hilbert space and linear operators, Banach algebras, C*- algebra theory, and von Neumann algebra theory. The volumes are numbered consecutively but indexed separately. Volume one was originally published by Academic Press in 1983. Annotation copyrighted by Book News, Inc., Portland, OR

Contents:

""Cover""; ""Title""; ""Copyright""; ""Contents""; ""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 L[sub(1)](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""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed April 11, 2015).

ISBN:

1-4704-2072-4