C-star-algebras and their automorphism groups

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This elegantly edited landmark edition of Gert KjïŽrgïŽrd 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 SïŽren 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 KjïŽrgïŽrd 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 SïŽren 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.