Real operator algebras /:
The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seeme...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, N.J. :
World Scientific,
©2003.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently. The aim of this text is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. |
| Beschreibung: | 1 online resource (xiii, 241 pages) |
| Bibliographie: | Includes bibliographical references (pages 233-235) and indexes. |
| ISBN: | 9789812795182 9812795189 1281935611 9781281935618 |
Internformat
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| 245 | 1 | 0 | |a Real operator algebras / |c Bingren Li. |
| 260 | |a River Edge, N.J. : |b World Scientific, |c ©2003. | ||
| 300 | |a 1 online resource (xiii, 241 pages) | ||
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| 505 | 0 | |a 1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces -- 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras -- 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras -- 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras -- 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras -- 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries -- 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case -- 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products -- 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory -- 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties. | |
| 520 | |a The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently. The aim of this text is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. | ||
| 650 | 0 | |a Banach algebras. |0 http://id.loc.gov/authorities/subjects/sh85011437 | |
| 650 | 0 | |a Operator algebras. |0 http://id.loc.gov/authorities/subjects/sh85095022 | |
| 650 | 6 | |a Algèbres normées. | |
| 650 | 6 | |a Algèbres de Banach. | |
| 650 | 6 | |a Algèbres d'opérateurs. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Banach algebras |2 fast | |
| 650 | 7 | |a Operator algebras |2 fast | |
| 650 | 7 | |a Operatoralgebra |2 gnd |0 http://d-nb.info/gnd/4129366-6 | |
| 700 | 1 | |a Li, Bingren, |d 1941- |1 https://id.oclc.org/worldcat/entity/E39PCjKDGQhtgW8RCt899RmHT3 |0 http://id.loc.gov/authorities/names/nr94022391 | |
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| contents | 1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces -- 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras -- 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras -- 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras -- 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras -- 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries -- 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case -- 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products -- 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory -- 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties. |
| ctrlnum | (OCoLC)825768141 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:25:09Z |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Li, Bingren, 1941- https://id.oclc.org/worldcat/entity/E39PCjKDGQhtgW8RCt899RmHT3 http://id.loc.gov/authorities/names/nr94022391 Real operator algebras / Bingren Li. River Edge, N.J. : World Scientific, ©2003. 1 online resource (xiii, 241 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 233-235) and indexes. Print version record. 1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces -- 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras -- 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras -- 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras -- 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras -- 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries -- 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case -- 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products -- 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory -- 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties. The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently. The aim of this text is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 Operator algebras. http://id.loc.gov/authorities/subjects/sh85095022 Algèbres normées. Algèbres de Banach. Algèbres d'opérateurs. MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Operator algebras fast Operatoralgebra gnd http://d-nb.info/gnd/4129366-6 Print version: Li, Bing₉ren, 1941- Real operator algebras. River Edge, N.J. : World Scientific, ©2003 9812383808 (DLC) 2005297495 (OCoLC)52851755 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235622 Volltext |
| spellingShingle | Li, Bingren, 1941- Real operator algebras / 1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces -- 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras -- 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras -- 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras -- 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras -- 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries -- 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case -- 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products -- 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory -- 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties. Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 Operator algebras. http://id.loc.gov/authorities/subjects/sh85095022 Algèbres normées. Algèbres de Banach. Algèbres d'opérateurs. MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Operator algebras fast Operatoralgebra gnd http://d-nb.info/gnd/4129366-6 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85011437 http://id.loc.gov/authorities/subjects/sh85095022 http://d-nb.info/gnd/4129366-6 |
| title | Real operator algebras / |
| title_auth | Real operator algebras / |
| title_exact_search | Real operator algebras / |
| title_full | Real operator algebras / Bingren Li. |
| title_fullStr | Real operator algebras / Bingren Li. |
| title_full_unstemmed | Real operator algebras / Bingren Li. |
| title_short | Real operator algebras / |
| title_sort | real operator algebras |
| topic | Banach algebras. http://id.loc.gov/authorities/subjects/sh85011437 Operator algebras. http://id.loc.gov/authorities/subjects/sh85095022 Algèbres normées. Algèbres de Banach. Algèbres d'opérateurs. MATHEMATICS Algebra Linear. bisacsh Banach algebras fast Operator algebras fast Operatoralgebra gnd http://d-nb.info/gnd/4129366-6 |
| topic_facet | Banach algebras. Operator algebras. Algèbres normées. Algèbres de Banach. Algèbres d'opérateurs. MATHEMATICS Algebra Linear. Banach algebras Operator algebras Operatoralgebra |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235622 |
| work_keys_str_mv | AT libingren realoperatoralgebras |