Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Combinatorial Set Theory of C-algebras / / by Ilijas Farah
| Combinatorial Set Theory of C-algebras / / by Ilijas Farah |
| Autore | Farah Ilijas |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (535 pages) |
| Disciplina | 512.55 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Logic, Symbolic and mathematical
Functional analysis Operator theory Associative rings Associative algebras Mathematical Logic and Foundations Functional Analysis Operator Theory Associative Rings and Algebras |
| ISBN | 3-030-27093-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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. |
| Record Nr. | UNINA-9910364957303321 |
Farah Ilijas
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model theory of C∗-algebras / / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter
| Model theory of C∗-algebras / / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter |
| Autore | Farah Ilijas |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (142 pages) |
| Disciplina | 512/.556 |
| Altri autori (Persone) |
HartBradd
LupiniMartino |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
C*-algebras
Model theory |
| ISBN |
9781470466268
1470466260 |
| Classificazione | 46L0546L3503C2003C9803E1503C25 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Continuous model theory -- 2.1. Preliminaries -- 2.2. Theories -- 2.3. Ultraproducts -- 2.3.1. Atomic and Elementary Diagrams -- 2.4. Elementary classes and preservation theorems -- 2.5. Elementary classes of \cstar-algebras -- 2.5.1. Abelian algebras -- 2.5.2. Non-abelian algebras -- 2.5.3. Real rank zero again -- 2.5.4. -subhomogeneous -- 2.5.5. Non- -subhomogeneous algebras -- 2.5.6. Tracial \cstar-algebras -- 2.5.7. \cstar-algebras with a character -- 2.6. Downward Löwenheim-Skolem -- 2.7. Tensorial absorption and elementary submodels -- 2.7.1. Strongly self-absorbing \cstar-algebras -- 2.7.2. Stable algebras -- Chapter 3. Definability and ^{\eq} -- 3.1. Expanding the definition of formula: definable predicates and functions -- 3.1.1. Definable predicates -- 3.2. Expanding the definition of formula: definable sets -- 3.3. Expanding the language: imaginaries -- Countable products -- Definable sets -- Quotients -- ^{\eq} and ^{\eq} -- 3.4. The use of continuous functional calculus -- 3.5. Definability of traces -- 3.5.1. Definability of Cuntz-Pedersen equivalence -- 3.6. Axiomatizability via definable sets -- 3.6.1. Projectionless and unital projectionless -- 3.6.2. Real rank zero revisited -- 3.6.3. Infinite \cstar-algebras -- 3.6.4. Finite and stably finite algebras -- 3.7. Invertible and non-invertible elements -- 3.8. Stable rank -- 3.9. Real rank -- 3.10. Tensor products -- 3.11. ₀( ) and ^{\eq} -- 3.12. ₁( ) and ^{\eq} -- 3.13. Co-elementarity -- 3.13.1. Abelian algebras -- 3.13.2. Infinite algebras -- 3.13.3. Algebras containing a unital copy of _{ }(\bbC) -- 3.13.4. Definability of sets of projections -- 3.13.5. Stable rank one -- 3.13.6. Real rank zero -- 3.13.7. Purely infinite simple \cstar-algebras -- 3.14. Some non-elementary classes of \cstar-algebras.
Chapter 4. Types -- 4.1. Types: the definition -- 4.1.1. Types as sets of conditions -- 4.2. Beth definability -- 4.3. Saturated models -- 4.4. MF algebras -- 4.5. Approximately divisible algebras -- Chapter 5. Approximation properties -- 5.1. Nuclearity -- 5.2. Completely positive contractive order zero maps -- 5.3. Nuclear dimension -- 5.4. Decomposition rank -- 5.5. Quasidiagonal algebras -- 5.6. Approximation properties and definability -- 5.7. Approximation properties and uniform families of formulas -- 5.7.1. Uniform families of formulas -- 5.8. Nuclearity, nuclear dimension and decomposition rank: First proof -- 5.9. Nuclearity, nuclear dimension and decomposition rank: Second proof -- 5.10. Simple \cstar-algebras -- 5.11. Popa algebras -- 5.12. Simple tracially AF algebras -- 5.13. Quasidiagonality -- 5.14. An application: Preservation by quotients -- 5.15. An application: Perturbations -- 5.16. An application: Preservation by inductive limits -- 5.17. An application: Borel sets of \cstar-algebras -- Chapter 6. Generic \cstar-algebras -- 6.1. Henkin forcing -- 6.2. Infinite forcing -- 6.3. Finite forcing -- 6.4. ∀∃-axiomatizability and existentially closed structures -- 6.5. Strongly self-absorbing algebras -- 6.6. Stably finite, quasidiagonal, and MF algebras -- Chapter 7. \cstar-algebras not elementarily equivalent to nuclear \cstar-algebras -- 7.1. Exact algebras -- 7.2. Definability of traces: the uniform strong Dixmier property -- 7.3. Elementary submodels of von Neumann algebras -- Chapter 8. The Cuntz semigroup -- 8.1. Cuntz subequivalence -- 8.2. Strict comparison of positive elements -- 8.3. The Toms-Winter conjecture -- 8.4. Radius of comparison -- Appendix A. \cstar-algebras -- Bibliography -- Index -- Back Cover. |
| Record Nr. | UNINA-9910953751803321 |
|
Farah Ilijas
|
||
| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||