Ebook: Noncommutative Probability

The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".

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This volume introduces the subject of noncommutative probability from a mathematical point of view based on the idea of generalising fundamental theorems in classical probability theory. It contains topics including von Neumann algebras, Fock spaces, free independence and Jordan algebras. Full proofs are given, and outlines are sketched where some background information is essential to follow the argument. The bibliography lists classical papers on the subject as well as recent titles, thus enabling further study.
This book is of interest to graduate students and researchers in functional analysis, von Neumann algebras, probability theory and stochastic calculus. Some previous knowledge of operator algebras and probability theory is assumed.

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This volume introduces the subject of noncommutative probability from a mathematical point of view based on the idea of generalising fundamental theorems in classical probability theory. It contains topics including von Neumann algebras, Fock spaces, free independence and Jordan algebras. Full proofs are given, and outlines are sketched where some background information is essential to follow the argument. The bibliography lists classical papers on the subject as well as recent titles, thus enabling further study.
This book is of interest to graduate students and researchers in functional analysis, von Neumann algebras, probability theory and stochastic calculus. Some previous knowledge of operator algebras and probability theory is assumed.

Content:
Front Matter....Pages i-xiv
Central Limit Theorem on L(H)....Pages 1-52
Probability on von Neumann Algebras....Pages 53-94
Free Independence....Pages 95-123
The Clifford Algebra....Pages 124-159
Stochastic Integrals....Pages 160-233
Conditional Mean Values....Pages 234-292
Jordan Algebras....Pages 293-315
Back Matter....Pages 317-353

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This volume introduces the subject of noncommutative probability from a mathematical point of view based on the idea of generalising fundamental theorems in classical probability theory. It contains topics including von Neumann algebras, Fock spaces, free independence and Jordan algebras. Full proofs are given, and outlines are sketched where some background information is essential to follow the argument. The bibliography lists classical papers on the subject as well as recent titles, thus enabling further study.
This book is of interest to graduate students and researchers in functional analysis, von Neumann algebras, probability theory and stochastic calculus. Some previous knowledge of operator algebras and probability theory is assumed.

Content:
Front Matter....Pages i-xiv
Central Limit Theorem on L(H)....Pages 1-52
Probability on von Neumann Algebras....Pages 53-94
Free Independence....Pages 95-123
The Clifford Algebra....Pages 124-159
Stochastic Integrals....Pages 160-233
Conditional Mean Values....Pages 234-292
Jordan Algebras....Pages 293-315
Back Matter....Pages 317-353
....