Bounded Symmetric Domains In Banach Spaces
Bounded Symmetric Domains In Banach Spaces

Author: Cho-ho Chu

Publisher: World Scientific

Published: 2020-09-10

Total Pages: 406

ISBN-13: 9811214123

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This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment of both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching applications of this realization in complex geometry and function theory are discussed.This monograph is intended as a convenient reference for researchers and graduate students in geometric analysis, infinite dimensional holomorphy as well as functional analysis and operator theory.

Nonlinear Semigroups, Fixed Points, And Geometry Of Domains In Banach Spaces
Nonlinear Semigroups, Fixed Points, And Geometry Of Domains In Banach Spaces

Author: Simeon Reich

Publisher: World Scientific

Published: 2005-07-12

Total Pages: 372

ISBN-13: 1783260211

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Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments./a

Finite or Infinite Dimensional Complex Analysis
Finite or Infinite Dimensional Complex Analysis

Author: Joji Kajiwara

Publisher: CRC Press

Published: 2019-05-07

Total Pages: 674

ISBN-13: 0429530005

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This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.

Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics
Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics

Author: Harald Upmeier

Publisher: American Mathematical Soc.

Published: 1987

Total Pages: 95

ISBN-13: 082180717X

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Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. This book describes some relevant results and puts them in a general framework.

Symmetric Banach Manifolds and Jordan C*-Algebras
Symmetric Banach Manifolds and Jordan C*-Algebras

Author: H. Upmeier

Publisher: Elsevier

Published: 2011-08-18

Total Pages: 457

ISBN-13: 0080872158

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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.

Multivariable Operator Theory
Multivariable Operator Theory

Author: Ernst Albrecht

Publisher: Springer Nature

Published: 2024-01-22

Total Pages: 893

ISBN-13: 3031505352

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Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Geometric Function Theory in Higher Dimension
Geometric Function Theory in Higher Dimension

Author: Filippo Bracci

Publisher: Springer

Published: 2018-03-24

Total Pages: 185

ISBN-13: 3319731262

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The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

M-Ideals in Banach Spaces and Banach Algebras
M-Ideals in Banach Spaces and Banach Algebras

Author: Peter Harmand

Publisher: Springer

Published: 2006-11-15

Total Pages: 390

ISBN-13: 3540477535

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This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.