Lectures on Von Neumann Algebras
Author: Serban Stratila
Publisher: Routledge
Published: 1979
Total Pages: 486
ISBN-13:
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Lectures on von Neumann Algebras
Author: Serban-Valentin Stratila
Publisher: Cambridge University Press
Published: 2019-05-09
Total Pages: 442
ISBN-13: 1108750222
DOWNLOAD EBOOKWritten 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.
Lectures on von Neumann Algebras
Author: Șerban Strătilă
Publisher: Cambridge University Press
Published: 2019-05-09
Total Pages: 441
ISBN-13: 1108496849
DOWNLOAD EBOOKThe text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
An Invitation to von Neumann Algebras
Author: V.S. Sunder
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 184
ISBN-13: 1461386691
DOWNLOAD EBOOKWhy 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.
Fields Medallists' Lectures
Author: Michael Atiyah
Publisher: World Scientific
Published: 1997-10-13
Total Pages: 644
ISBN-13: 9814497517
DOWNLOAD EBOOKAlthough 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.
Modular Theory in Operator Algebras
Author: Serban Stratila
Publisher: Cambridge University Press
Published: 2020-12-03
Total Pages: 461
ISBN-13: 1108489605
DOWNLOAD EBOOKThe 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.
Lectures on Von Neumann Algebras
Author: David M. Topping
Publisher:
Published: 1971
Total Pages: 136
ISBN-13:
DOWNLOAD EBOOKC*-Algebras and W*-Algebras
Author: Shoichiro Sakai
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 271
ISBN-13: 3642619932
DOWNLOAD EBOOKFrom the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews
Lectures on Amenability
Author: Volker Runde
Publisher: Springer Science & Business Media
Published: 2002-01-10
Total Pages: 316
ISBN-13: 9783540428527
DOWNLOAD EBOOKThe 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.
C*-Algebras and Operator Theory
Author: Gerald J. Murphy
Publisher: Academic Press
Published: 2014-06-28
Total Pages: 297
ISBN-13: 0080924964
DOWNLOAD EBOOKThis book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
