Positivity And Noncommutative Analysis

Author : Gerard Buskes,Marcel de Jeu,Peter Dodds,Anton Schep,Fedor Sukochev,Jan van Neerven,Anthony Wickstead
Publisher : Springer
Page : 604 pages
File Size : 50,7 Mb
Release : 2019-08-09
Category : Mathematics
ISBN : 9783030108502

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Positivity and Noncommutative Analysis by Gerard Buskes,Marcel de Jeu,Peter Dodds,Anton Schep,Fedor Sukochev,Jan van Neerven,Anthony Wickstead Pdf

Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Glück, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernández, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lü, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Román, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 46,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : R. Nagel,U. Schlotterbeck,M.P.H. Wolff
Publisher : Elsevier
Page : 274 pages
File Size : 51,9 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 0080872336

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Aspects of Positivity in Functional Analysis by R. Nagel,U. Schlotterbeck,M.P.H. Wolff Pdf

The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order theory in analysis and show the possibilities of order-theoretical argumentation. The following areas are discussed: potential theory, partial differential operators of second order, Schrodinger operators, theory of convexity, one-parameter semigroups, Lie algebras, Markov processes, operator-algebras, noncommutative integration and geometry of Banach spaces.

Author : Peter G. Dodds,Ben de Pagter,Fedor A. Sukochev
Publisher : Springer Nature
Page : 583 pages
File Size : 54,5 Mb
Release : 2024-01-19
Category : Mathematics
ISBN : 9783031496547

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Noncommutative Integration and Operator Theory by Peter G. Dodds,Ben de Pagter,Fedor A. Sukochev Pdf

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.

Author : Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot
Publisher : Birkhäuser
Page : 283 pages
File Size : 47,7 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319291161

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Noncommutative Analysis, Operator Theory and Applications by Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot Pdf

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Author : Siu-Ah Ng
Publisher : World Scientific
Page : 339 pages
File Size : 48,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814287555

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Nonstandard Methods in Functional Analysis by Siu-Ah Ng Pdf

In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.

Author : Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 48,8 Mb
Release : 2023-04-03
Category : Mathematics
ISBN : 9783110700176

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Trace Formulas by Steven Lord,Edward McDonald,Fedor Sukochev,Dmitriy Zanin Pdf

This volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes’ noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes’ character formula concerning the Hochschild class of the Chern character.

Author : Palle Jorgensen,Steen Pedersen,Feng Tian
Publisher : Springer
Page : 231 pages
File Size : 44,6 Mb
Release : 2016-07-08
Category : Mathematics
ISBN : 9783319397801

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Extensions of Positive Definite Functions by Palle Jorgensen,Steen Pedersen,Feng Tian Pdf

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

Author : Karim Boulabiar,Gerard Buskes,Abdelmajid Triki
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 48,5 Mb
Release : 2007-12-16
Category : Mathematics
ISBN : 9783764384784

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Positivity by Karim Boulabiar,Gerard Buskes,Abdelmajid Triki Pdf

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.

Author : Marek Bożejko
Publisher : Unknown
Page : 334 pages
File Size : 55,6 Mb
Release : 2007
Category : Free probability theory
ISBN : UOM:39015075633761

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Noncommutative Harmonic Analysis with Applications to Probability by Marek Bożejko Pdf

Author : Rajendra Bhatia
Publisher : Princeton University Press
Page : 264 pages
File Size : 51,8 Mb
Release : 2015-09-01
Category : Mathematics
ISBN : 9780691168258

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Positive Definite Matrices by Rajendra Bhatia Pdf

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.

Author : Harold Garth Dales
Publisher : Springer Nature
Page : 452 pages
File Size : 52,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031445323

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Banach Function Algebras, Arens Regularity, and BSE Norms by Harold Garth Dales Pdf

Author : Eder Kikianty,Mokhwetha Mabula,Miek Messerschmidt,Jan Harm van der Walt,Marten Wortel
Publisher : Springer Nature
Page : 321 pages
File Size : 45,8 Mb
Release : 2021-07-22
Category : Mathematics
ISBN : 9783030709747

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Positivity and its Applications by Eder Kikianty,Mokhwetha Mabula,Miek Messerschmidt,Jan Harm van der Walt,Marten Wortel Pdf

This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.

Author : Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek
Publisher : Springer Nature
Page : 467 pages
File Size : 48,9 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030446512

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Operator Algebras, Toeplitz Operators and Related Topics by Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek Pdf

This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 45,7 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 9780821823149

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Noncommutative Microlocal Analysis by Michael Eugene Taylor Pdf