Lectures On Selected Topics In Von Neumann Algebras
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Lectures On Selected Topics In Von Neumann Algebras
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Author : Fumio Hiai
language : en
Publisher:
Release Date : 2021
Lectures On Selected Topics In Von Neumann Algebras written by Fumio Hiai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Finite Von Neumann Algebras And Masas
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Author : Allan Sinclair
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-26
Finite Von Neumann Algebras And Masas written by Allan Sinclair and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-26 with Mathematics categories.
The first book devoted to the general theory of finite von Neumann algebras.
Lectures On Von Neumann Algebras
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Author : Șerban Strătilă
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-09
Lectures On Von Neumann Algebras written by Șerban Strătilă and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-09 with Mathematics categories.
The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
Lectures On Von Neumann Algebras
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Author : Serban-Valentin Stratila
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-09
Lectures On Von Neumann Algebras written by Serban-Valentin Stratila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-09 with Mathematics categories.
Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
Quantum F Divergences In Von Neumann Algebras
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Author : Fumio Hiai
language : en
Publisher: Springer Nature
Release Date : 2021-01-26
Quantum F Divergences In Von Neumann Algebras written by Fumio Hiai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Science categories.
Relative entropy has played a significant role in various fields of mathematics and physics as the quantum version of the Kullback–Leibler divergence in classical theory. Many variations of relative entropy have been introduced so far with applications to quantum information and related subjects. Typical examples are three different classes, called the standard, the maximal, and the measured f-divergences, all of which are defined in terms of (operator) convex functions f on (0,∞) and have respective mathematical and information theoretical backgrounds. The α-Rényi relative entropy and its new version called the sandwiched α-Rényi relative entropy have also been useful in recent developments of quantum information. In the first half of this monograph, the different types of quantum f-divergences and the Rényi-type divergences mentioned above in the general von Neumann algebra setting are presented for study. While quantum information has been developing mostly in the finite-dimensional setting, it is widely believed that von Neumann algebras provide the most suitable framework in studying quantum information and related subjects. Thus, the advance of quantum divergences in von Neumann algebras will be beneficial for further development of quantum information. Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum f-divergences is explained, thus extending and strengthening Petz' previous work. For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided.
Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics
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Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2016-05-24
Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Science categories.
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.
Modular Theory In Operator Algebras
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Author : Şerban Strǎtilǎ
language : en
Publisher: Cambridge University Press
Release Date : 2020-12-03
Modular Theory In Operator Algebras written by Şerban Strǎtilǎ and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-03 with Mathematics categories.
Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.
Lectures On Amenability
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Author : Volker Runde
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-10
Lectures On Amenability written by Volker Runde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-10 with Mathematics categories.
The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
Lectures On Von Neumann Algebras
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Author : David M. Topping
language : en
Publisher:
Release Date : 1971
Lectures On Von Neumann Algebras written by David M. Topping and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Noncommutative Integration And Operator Theory
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Author : Peter G. Dodds
language : en
Publisher: Springer Nature
Release Date : 2024-01-19
Noncommutative Integration And Operator Theory written by Peter G. Dodds and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.