Author: Sergey Neshveyev
Publisher: Springer Science & Business Media
ISBN: 3540346732
Category : Mathematics
Languages : en
Pages : 294
Book Description
The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
Dynamical Entropy in Operator Algebras
Author: Sergey Neshveyev
Publisher: Springer Science & Business Media
ISBN: 3540346732
Category : Mathematics
Languages : en
Pages : 294
Book Description
The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
Publisher: Springer Science & Business Media
ISBN: 3540346732
Category : Mathematics
Languages : en
Pages : 294
Book Description
The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
Classification of Nuclear C*-Algebras. Entropy in Operator Algebras
Author: M. Rordam
Publisher: Springer Science & Business Media
ISBN: 3662048256
Category : Mathematics
Languages : en
Pages : 206
Book Description
to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.
Publisher: Springer Science & Business Media
ISBN: 3662048256
Category : Mathematics
Languages : en
Pages : 206
Book Description
to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.
Entropy in operator algebras
Recent Advances in Operator Theory and Operator Algebras
Author: Hari Bercovici
Publisher: CRC Press
ISBN: 1351643037
Category : Mathematics
Languages : en
Pages : 219
Book Description
This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.
Publisher: CRC Press
ISBN: 1351643037
Category : Mathematics
Languages : en
Pages : 219
Book Description
This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.
Quantum Entropy and Its Use
Author: M. Ohya
Publisher: Springer Science & Business Media
ISBN: 9783540208068
Category : Science
Languages : en
Pages : 368
Book Description
Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.
Publisher: Springer Science & Business Media
ISBN: 9783540208068
Category : Science
Languages : en
Pages : 368
Book Description
Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.
Classification of Nuclear C*-algebras. Entropy in Operator Algebras
Author: Mikael Rørdam
Publisher:
ISBN:
Category : C*-algebras
Languages : en
Pages : 198
Book Description
Publisher:
ISBN:
Category : C*-algebras
Languages : en
Pages : 198
Book Description
Dynamical Approximation Entropies and Topological Entropy in Operator Algebras
Author: Dan V. Voiculescu
Publisher:
ISBN:
Category : Operator algebras
Languages : en
Pages : 31
Book Description
Publisher:
ISBN:
Category : Operator algebras
Languages : en
Pages : 31
Book Description
Classification of Nuclear C*-algebras. Entropy in Operator Algebras
Operator Algebras and Non-commutative Geometry: Classification of nuclear c*-Algebras. Entropy in operator algebras
Theory of Operator Algebras I
Author: M. Takesaki
Publisher: Springer
ISBN: 9783540422488
Category : Mathematics
Languages : en
Pages : 415
Book Description
Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.
Publisher: Springer
ISBN: 9783540422488
Category : Mathematics
Languages : en
Pages : 415
Book Description
Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.