C-star-algebras and their automorphism groups

This elegantly edited landmark edition of Gert KjïÅ1⁄2rgïÅ1⁄2rd Pedersen's C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen's monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of SïÅ1⁄2ren Eilers and Dorte Olesen, the second edition modernizes Pedersen's work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author's later work. Read more... Abstract: This elegantly edited landmark edition of Gert KjïÅ1⁄2rgïÅ1⁄2rd Pedersen's C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen's monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of SïÅ1⁄2ren Eilers and Dorte Olesen, the second edition modernizes Pedersen's work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author's later work Content: Intro C*-Algebras and Their Automorphism Groups Contents Biography Gert Kjærgård Pedersen (1940-2004) Author's Preface Editors' Preface 1 Abstract C*-Algebras 1.1 Spectral Theory 1.1.1 1.1.2 1.1.3 Proposition 1.1.4 1.1.5 Lemma 1.1.6 1.1.7 Theorem 1.1.8 Proposition 1.1.9 1.1.10 1.1.11 1.1.12 Proposition 1.1.13 1.1.14 Author's notes and remarks 1.1.15 Editors' notes and remarks 1.2 Examples 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 Author's notes and remarks 1.2.7 Editors' notes and remarks 1.2.8 1.2.9 1.3 Positive Elements and Order 1.3.1 Lemma 1.3.2. 1.3.3 Theorem1.3.4 1.3.5 Proposition 1.3.6 Proposition 1.3.7 1.3.8 Proposition 1.3.9 Proposition 1.3.10 1.3.11 Proposition 1.3.12 Author's notes and remarks 1.3.13 Editors' notes and remarks 1.3.14 Lemma 1.3.15 Theorem 1.4 Approximate Units and Factorization Theorems 1.4.1 1.4.2 Theorem 1.4.3 1.4.4 Lemma 1.4.5 Proposition 1.4.6 1.4.7 Proposition 1.4.8 Proposition 1.4.9 1.4.10 Proposition 1.4.11 Author's notes and remarks 1.4.12 Editors' notes and remarks 1.5 Hereditary Algebras, Ideals, and Quotients 1.5.1 1.5.2 Theorem 1.5.3 Corollary 1.5.4 Lemma 1.5.5 Corollary. 1.5.61.5.7 Theorem 1.5.8 Corollary 1.5.9 Proposition 1.5.10 Proposition 1.5.11 Corollary 1.5.12 Author's notes and remarks 1.5.13 Editors' notes and remarks 1.5.14 Lemma 1.5.15 Editors' notes and remarks 1.5.16 2 Concrete C*-Algebras 2.1 Topologies on B(H) 2.1.1 2.1.2 2.1.3 Lemma 2.1.4 2.1.5 Theorem 2.1.6 Corollary 2.1.7 Author's notes and remarks 2.2 von Neumann's Bicommutant Theorem 2.2.1 2.2.2 Theorem 2.2.3 Lemma 2.2.4 2.2.5 Corollary 2.2.6 2.2.7 2.2.8 2.2.9 Proposition 2.2.10 2.2.11 Author's notes and remarks 2.3 Kaplansky's Density Theorem 2.3.1. 2.3.2 Proposition2.3.3 Theorem 2.3.4 Author's notes and remarks 2.4 The Up-Down Theorem 2.4.1 2.4.2 Lemma 2.4.3 Theorem 2.4.4 Theorem 2.4.5 Author's notes and remarks 2.5 Normal Morphisms and Ideals 2.5.1 2.5.2 Proposition 2.5.4 Proposition 2.5.3 Theorem 2.5.5 Corollary 2.5.6 Author's notes and remarks 2.5.7 Editors' notes and remarks 2.6 The Central Cover 2.6.1 2.6.2 2.6.3 Lemma 2.6.4 Lemma 2.6.5 Lemma 2.6.6 Lemma 2.6.7 Proposition 2.6.8 Corollary 2.6.9 Author's notes and remarks 2.7 A Generalization of Lusin's Theorem 2.7.1 2.7.2 Lemma 2.7.3 Theorem. 2.7.4 Corollary2.7.5 Theorem 2.7.6 Author's notes and remarks 2.7.7 Editors' notes and remarks 2.8 Maximal Commutative Subalgebras 2.8.1 2.8.2 2.8.3 Proposition 2.8.4 Theorem 2.8.5 Lemma 2.8.6 Lemma 2.8.7 2.8.8 Corollary 2.8.9 Author's notes and remarks 2.8.10 Editors' notes and remarks 2.9 Universal C*-Algebras 2.9.1 Editors' notes and remarks 2.9.2 2.9.3 Theorem 2.9.4 2.9.5 2.9.6 3 Functionals and Representations 3.1 Positive Functionals 3.1.1 3.1.2 3.1.3 Theorem 3.1.4 Proposition 3.1.5 Lemma 3.1.6 Proposition 3.1.7 Author's notes and remarks.

This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen’s monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen’s work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author’s later work.

• Covers basic C*-algebras theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author
• Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory
• Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout
• Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups
• Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography

This elegantly edited landmark edition of Gert KjïÅưrgïÅưrd Pedersen's C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen's monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of SïÅưren Eilers and Dorte Olesen, the second edition modernizes Pedersen's work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author's later work