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Combinatorial set theory of C*-algebras

Farah, Ilijas.

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Combinatorial set theory of C*-algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	Combinatorial set theory of C*-algebras/ by Ilijas Farah.
Author:	Farah, Ilijas.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xxx, 517 p. :ill., digital ;24 cm.
[NT 15003449]:	1. C-algebras, Abstract and Concrete -- 2. Examples and Constructions of C-algebras -- 3. Representations of C-algebras -- 4. Tracial States and Representations of C-algebras -- 5. Irreducible Representations of C-algebras -- Part II Set Theory and Nonseparable C-algebras -- 6. Infinitary Combinatorics, I -- 7. Infinitary Combinatorics, II: The Metric Case -- 8. Additional Set-Theoretic Axioms -- 9. Set Theory and Quotients -- 10. Constructions of Nonseparable C-algebras, I: Graph CCR Algebras -- 11. Constructions of Nonseparable C-algebras, II -- Part III Massive Quotient C-algebras -- 12. The Calkin Algebra -- 13. Multiplier Algebras and Coronas -- 14. Gaps and Incompactness -- 15. Degree-1 Saturation -- 16. Full Saturation -- 17. Automorphisms of Massive Quotient C-Algebras -- Part IV Appendices -- A. Axiomatic Set Theory -- B. Descriptive Set Theory -- C. Functional Analysis -- D. Model Theory -- References -- Index -- List of Symbols.
Contained By:	Springer eBooks
Subject:	C*-algebras. -
Online resource:	https://doi.org/10.1007/978-3-030-27093-3
ISBN:	9783030270933

Combinatorial set theory of C*-algebras
Farah, Ilijas.

Combinatorial set theory of C*-algebras[electronic resource] /by Ilijas Farah. - Cham :Springer International Publishing :2019. - xxx, 517 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

1. C*-algebras, Abstract and Concrete -- 2. Examples and Constructions of C*-algebras -- 3. Representations of C*-algebras -- 4. Tracial States and Representations of C*-algebras -- 5. Irreducible Representations of C*-algebras -- Part II Set Theory and Nonseparable C*-algebras -- 6. Infinitary Combinatorics, I -- 7. Infinitary Combinatorics, II: The Metric Case -- 8. Additional Set-Theoretic Axioms -- 9. Set Theory and Quotients -- 10. Constructions of Nonseparable C*-algebras, I: Graph CCR Algebras -- 11. Constructions of Nonseparable C*-algebras, II -- Part III Massive Quotient C*-algebras -- 12. The Calkin Algebra -- 13. Multiplier Algebras and Coronas -- 14. Gaps and Incompactness -- 15. Degree-1 Saturation -- 16. Full Saturation -- 17. Automorphisms of Massive Quotient C*-Algebras -- Part IV Appendices -- A. Axiomatic Set Theory -- B. Descriptive Set Theory -- C. Functional Analysis -- D. Model Theory -- References -- Index -- List of Symbols.

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.

ISBN: 9783030270933

Standard No.: 10.1007/978-3-030-27093-3doiSubjects--Topical Terms:

542530
C*-algebras.

LC Class. No.: QA326 / .F37 2019

Dewey Class. No.: 512.554

Combinatorial set theory of C*-algebras
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100 1 $a Farah, Ilijas. $3 3454457
245 1 0 $a Combinatorial set theory of C*-algebras $h [electronic resource] / $c by Ilijas Farah.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxx, 517 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 1. C*-algebras, Abstract and Concrete -- 2. Examples and Constructions of C*-algebras -- 3. Representations of C*-algebras -- 4. Tracial States and Representations of C*-algebras -- 5. Irreducible Representations of C*-algebras -- Part II Set Theory and Nonseparable C*-algebras -- 6. Infinitary Combinatorics, I -- 7. Infinitary Combinatorics, II: The Metric Case -- 8. Additional Set-Theoretic Axioms -- 9. Set Theory and Quotients -- 10. Constructions of Nonseparable C*-algebras, I: Graph CCR Algebras -- 11. Constructions of Nonseparable C*-algebras, II -- Part III Massive Quotient C*-algebras -- 12. The Calkin Algebra -- 13. Multiplier Algebras and Coronas -- 14. Gaps and Incompactness -- 15. Degree-1 Saturation -- 16. Full Saturation -- 17. Automorphisms of Massive Quotient C*-Algebras -- Part IV Appendices -- A. Axiomatic Set Theory -- B. Descriptive Set Theory -- C. Functional Analysis -- D. Model Theory -- References -- Index -- List of Symbols.
520 $a 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.
650 0 $a C*-algebras. $3 542530
650 0 $a Combinatorial set theory. $3 1566725
650 1 4 $a Mathematical Logic and Foundations. $3 892656
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Associative Rings and Algebras. $3 897405
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-3-030-27093-3
950 $a Mathematics and Statistics (Springer-11649)