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Operator Algebras, Operator Theory and Applications
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Symmetric Banach Manifolds and Jordan C*-Algebras
This book links two of the most active research areas in present day mathematics, namely Infinite Dimensional Holomorphy (on Banach spaces) and the theory of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a systematic way a wealth of recent results which are so far only accessible in research journals and contains additional original contributions. Using Banach Lie groups and Banach Lie algebras, a theory of transformation groups on infinite dimensional manifolds is presented which covers many important examples such as Grassmann manifolds and the unit balls of operator algebras. The theory also has potential importance for mathematical physics by providing foundations for the construction of infinite dimensional curved phase spaces in quantum field theory.
Perspectives on Quantization
This book presents the proceedings of a 1996 Joint Summer Research Conference sponsored by AMS-IMS-SIAM on "Quantization" held at Mount Holyoke College (Northampton, MA). The purpose of this conference was to bring together researchers focusing on various mathematical aspects of quantization. In the early work of Weyl and von Neumann at the beginning of the quantum era, the setting for this enterprise was operators on Hilbert space. This setting has been expanded, especially over the past decade, to involve C*-algebras - noncommutative differential geometry and noncommutative harmonic analysis - as well as more general algebras and infinite-dimensional manifolds. The applications now include...
A Panorama of Modern Operator Theory and Related Topics
This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
Function Spaces, Interpolation Theory and Related Topics
This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.
Function Spaces
This proceedings volume presents 36 papers given by leading experts during the Third Conference on Function Spaces held at Southern Illinois University at Edwardsville. A wide range of topics in the subject area are covered. Most papers are written for nonexperts, so the book can serve as a good introduction to the topic for those interested in this area. The book presents the following broad range of topics, including spaces and algebras of analytic functions of one and of many variables, $Lp$ spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces and related subjects. Known results, open problems, and new discoveries are featured. At the time of publication, information about the book, the conference, and a list and pictures of contributors are available on the Web at www.siue.edu/MATH/conference.htm.
Multivariable Operator Theory
This is a collection of papers presented at a conference on multivariable operator theory. The articles contain contributions to a variety of areas and topics which may be viewed as forming an emerging new subject. This subject involves the study of geometric rather than topological invariants associated with the general theme of operator theory in several variables. This collection will spur further discussion among the different research groups.
Interaction Between Functional Analysis, Harmonic Analysis, and Probability
Based on a conference on the interaction between functional analysis, harmonic analysis and probability theory, this work offers discussions of each distinct field, and integrates points common to each. It examines developments in Fourier analysis, interpolation theory, Banach space theory, probability, probability in Banach spaces, and more.
Jordan Triple Systems in Complex and Functional Analysis
This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.
