Modular Theory in Operator Algebras

Modular Theory in Operator Algebras
Author: Şerban Strǎtilǎ
Publisher: Cambridge University Press
Total Pages: 461
Release: 2020-12-03
Genre: Mathematics
ISBN: 1108489605

Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.

Lectures on von Neumann Algebras

Lectures on von Neumann Algebras
Author: Serban-Valentin Stratila
Publisher: Cambridge University Press
Total Pages: 442
Release: 2019-05-09
Genre: Mathematics
ISBN: 1108750222

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.

Lectures on von Neumann Algebras

Lectures on von Neumann Algebras
Author: Șerban Strătilă
Publisher: Cambridge University Press
Total Pages: 441
Release: 2019-05-09
Genre: Mathematics
ISBN: 1108496849

The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.

Petr Hájek on Mathematical Fuzzy Logic

Petr Hájek on Mathematical Fuzzy Logic
Author: Franco Montagna
Publisher: Springer
Total Pages: 324
Release: 2014-09-23
Genre: Mathematics
ISBN: 3319062336

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Matrix Computations and Semiseparable Matrices

Matrix Computations and Semiseparable Matrices
Author: Raf Vandebril
Publisher: JHU Press
Total Pages: 594
Release: 2008-01-14
Genre: Mathematics
ISBN: 0801896797

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Asymptotic Methods in Stochastics

Asymptotic Methods in Stochastics
Author: M. Csörgö
Publisher: American Mathematical Soc.
Total Pages: 546
Release: 2004
Genre: Mathematics
ISBN: 0821835610

Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations
Author: Juha Heinonen
Publisher: Courier Dover Publications
Total Pages: 417
Release: 2018-05-16
Genre: Mathematics
ISBN: 048682425X

A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.