Recurrence, transience, and poisson boundaries in operator algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Verl. Dr. Hut
2014
|
| Ausgabe: | 1. Aufl. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 138 S. |
| ISBN: | 9783843917414 |
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| 245 | 1 | 0 | |a Recurrence, transience, and poisson boundaries in operator algebras |c von Andreas Gärtner |
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Datensatz im Suchindex
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| adam_text | Recurrence, Transience,
and Poisson Boundaries
in Operator Algebras
Vom Fachbereich Mathematik der Technischen
Universität Darmstadt zur Erlangung des
Grades eines Doktors der Naturwissenschaften
(Dr rer nat ) genehmigte
Dissertation
von
Dipl -Math Andreas Gärtner
aus Wiesbaden-Sonnenberg
Referent: Prof Dr B Kümmerer
Korreferent: Prof Dr R Gohm
Tag der Einreichung: 24 April 2014
Tag der mündlichen Prüfung: 8 Juli 2014
Darmstadt, 2014
D 17
Contents
Preface v
Introduction v
Overview vii
Einleitung x
Zusammenfassung xii
Danksagung xv
1 Fundamentals in Operator Algebras and Probability 1
1 1 General Notation 1
1 2 Operator Algebras 3
1 3 Hereditary Convex Cones and C*-Subalgebras 7
1 4 Completely Positive Maps 8
1 5 (Probabilistic) Potential Theory 11
2 Markov Chains and Operators 17
2 1 Markov Chains on Countable State Spaces 18
2 2 Towards Quantization: Algebraic Reformulations 20
2 3 Quantum Markov Operators 22
2 4 The Lattice of superharmonic projections 24
3 Recurrent and Transient Projections and Subalgebras 27
3 1 Potentials and Transient Projections 28
3 2 Recurrent Projections 35
3 3 Fixing an Initial State: er-Finite Algebras 39
3 4 The Finite Dimensional Case 43
xvii
xviii CONTENTS
3 5 Markov Operators on SSiM1) 45
3 6 Automorphisms on 56
3 7 Unital Completely Positive Maps on C*-Algebras 66
4 Idempotent Maps 73
4 1 The Structure of Idempotent Markov Operators 74
4 2 The Choi-Effros Product 79
4 3 Quotients with Transient Subalgebras 82
5 Poisson Boundaries for Markov Operators 91
5 1 Probabilistic Poisson Boundaries 92
5 2 Non-Commutative Poisson Boundaries 93
5 3 Boundaries for Weak* Mean Ergodic Maps 101
6 Special classes of Markov operators 109
6 1 Entanglement Breaking Channels 109
6 2 The Baby Maser 114
Bibliography 123
List of Notations 129
Index 133
|
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| spelling | Gärtner, Andreas Verfasser (DE-588)1058695096 aut Recurrence, transience, and poisson boundaries in operator algebras von Andreas Gärtner 1. Aufl. München Verl. Dr. Hut 2014 XVII, 138 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Darmstadt, Techn. Univ., Diss., 2014 (DE-588)4113937-9 Hochschulschrift gnd-content HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027602557&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gärtner, Andreas Recurrence, transience, and poisson boundaries in operator algebras |
| subject_GND | (DE-588)4113937-9 |
| title | Recurrence, transience, and poisson boundaries in operator algebras |
| title_auth | Recurrence, transience, and poisson boundaries in operator algebras |
| title_exact_search | Recurrence, transience, and poisson boundaries in operator algebras |
| title_full | Recurrence, transience, and poisson boundaries in operator algebras von Andreas Gärtner |
| title_fullStr | Recurrence, transience, and poisson boundaries in operator algebras von Andreas Gärtner |
| title_full_unstemmed | Recurrence, transience, and poisson boundaries in operator algebras von Andreas Gärtner |
| title_short | Recurrence, transience, and poisson boundaries in operator algebras |
| title_sort | recurrence transience and poisson boundaries in operator algebras |
| topic_facet | Hochschulschrift |
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