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Author : Șerban Strătilă,Laszlo Zsido
Publisher : Cambridge University Press
Page : 441 pages
File Size : 46,6 Mb
Release : 2019-05-09
Category : Mathematics
ISBN : 9781108496841
The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
Author : David M. Topping
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 1969
Category : Electronic
ISBN : OCLC:977048770
Author : Fumio Hiai
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2021
Category : Electronic
ISBN : 3985470049
Author : Fumio Hiai
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2021
Category : Von Neumann algebras
ISBN : 3985475040
Author : Karl Heinrich Hofmann
Publisher : Springer
Page : 816 pages
File Size : 53,8 Mb
Release : 1972
Category : Algebras, Linear
ISBN : UCSC:32106002287503
Author : William Arveson
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 44,9 Mb
Release : 1984
Category : Mathematics
ISBN : 0821889001
This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.
Author : V.S. Sunder
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461386698
Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and K-Theory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any case, it is just what its title proclaims it to be -- an invitation to the exciting world of von Neumann algebras. It is hoped that after perusing this book, the reader might be tempted to fill in the numerous (and technically, capacious) gaps in this exposition, and to delve further into the depths of the theory. For the expert, it suffices to mention here that after some preliminaries, the book commences with the Murray - von Neumann classification of factors, proceeds through the basic modular theory to the III). classification of Connes, and concludes with a discussion of crossed-products, Krieger's ratio set, examples of factors, and Takesaki's duality theorem.
Author : B. V. Rajarama Bhat,George A. Elliott,Peter A. Fillmore
Publisher : American Mathematical Soc.
Page : 337 pages
File Size : 43,5 Mb
Release : 1999
Category : C*-algebras
ISBN : 9780821808214
This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.
Author : Serban Stratila
Publisher : Cambridge University Press
Page : 461 pages
File Size : 42,8 Mb
Release : 2020-12-03
Category : Mathematics
ISBN : 9781108489607
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsid ) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.
Author : Michael Atiyah,Daniel Iagolnitzer
Publisher : World Scientific
Page : 644 pages
File Size : 51,9 Mb
Release : 1997-10-13
Category : Mathematics
ISBN : 9789814497510
Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.
Author : Karl H. Hofmann
Publisher : Springer
Page : 793 pages
File Size : 42,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540371175
Author : Serban-Valentin Stratila,Laszlo Zsido
Publisher : Cambridge University Press
Page : 442 pages
File Size : 47,6 Mb
Release : 2019-05-09
Category : Mathematics
ISBN : 9781108750226
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.
Author : Adrian Ocneanu
Publisher : Lecture Notes in Mathematics
Page : 130 pages
File Size : 45,6 Mb
Release : 1985-08
Category : Mathematics
ISBN : UOM:39015049294989
Author : Volker Runde
Publisher : Springer
Page : 302 pages
File Size : 46,6 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540455608
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.
Author : John von Neumann
Publisher : Princeton University Press
Page : 312 pages
File Size : 47,5 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883950
In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
