An Introduction to Operator Algebras

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CRC Press, May 27, 1993 - Mathematics - 176 pages
An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.
 

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L^\infty functional calculus

Contents

The Spectrum
15
Examples of Maximal Ideal Spaces
34
Commutative CAlgebras
55
Polar Decomposition
71
Positive Linear Functionals and States
77
The GNS Construction
84
NonUnital CAlgebras
89
Won Neumann Algebras
97
The Kaplansky Density Theorem
113
The Borel Functional Calculus
118
Lš as a von Neumann Algebra
124
Abelian von Neumann Algebras
129
The LFunctional Calculus
134
Equivalence of Projections
140
A Partial Ordering
145
Type Decomposition
149

Strong and WeakOperator Topologies
98
Existence of Projections
103
The Double Commutant Theorem
108

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