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C*-代数的组合集理论-Combinatorial Set Theory of C*-algebras

上传于 2020-03-02 49次下载 4700次围观
标题(title):Combinatorial Set Theory of C*-algebras
作者(author):Ilijas Farah
出版社(publisher):Springer International Publishing
大小(size):7 MB (7840519 bytes)

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Table of contents :
Front Matter ....Pages i-xxx
Front Matter ....Pages 1-1
C∗-algebras, Abstract, and Concrete (Ilijas Farah)....Pages 3-46
Examples and Constructions of C∗-algebras (Ilijas Farah)....Pages 47-78
Representations of C∗-algebras (Ilijas Farah)....Pages 79-120
Tracial States and Representations of C∗-algebras (Ilijas Farah)....Pages 121-136
Irreducible Representations of C∗-algebras (Ilijas Farah)....Pages 137-174
Front Matter ....Pages 175-175
Infinitary Combinatorics I (Ilijas Farah)....Pages 177-197
Infinitary Combinatorics II: The Metric Case (Ilijas Farah)....Pages 199-216
Additional Set-Theoretic Axioms (Ilijas Farah)....Pages 217-239
Set Theory and Quotients (Ilijas Farah)....Pages 241-273
Constructions of Nonseparable C∗-algebras, I: Graph CCR Algebras (Ilijas Farah)....Pages 275-299
Constructions of Nonseparable C∗-algebras, II (Ilijas Farah)....Pages 301-310
Front Matter ....Pages 311-311
The Calkin Algebra (Ilijas Farah)....Pages 313-336
Multiplier Algebras and Coronas (Ilijas Farah)....Pages 337-348
Gaps and Incompactness (Ilijas Farah)....Pages 349-365
Degree-1 Saturation (Ilijas Farah)....Pages 367-392
Full Saturation (Ilijas Farah)....Pages 393-420
Automorphisms of Massive Quotient C∗-algebras (Ilijas Farah)....Pages 421-453
Back Matter ....Pages 455-517
C*-代数的组合集理论-Combinatorial Set Theory of C*-algebras
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