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Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

Author : Werner Ricker

Publisher : Springer

Page : 173 pages

File Size : 21,80 MB

Release : 2006-11-14

Category : Mathematics

ISBN : 3540482792

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Book Description

This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.



Positivity

Author : Karim Boulabiar

Publisher : Springer Science & Business Media

Page : 282 pages

File Size : 34,63 MB

Release : 2007-12-16

Category : Mathematics

ISBN : 3764384786

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Book Description

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.



Loeb Measures in Practice: Recent Advances

Author : Nigel J. Cutland

Publisher : Springer

Page : 118 pages

File Size : 26,90 MB

Release : 2004-10-11

Category : Mathematics

ISBN : 3540445315

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Book Description

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.



Optimal Domain and Integral Extension of Operators

Author : S. Okada

Publisher : Springer Science & Business Media

Page : 406 pages

File Size : 46,98 MB

Release : 2008-09-09

Category : Mathematics

ISBN : 3764386487

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Book Description

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.



Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Author : Martin Fuchs

Publisher : Springer Science & Business Media

Page : 284 pages

File Size : 45,99 MB

Release : 2000-12-12

Category : Mathematics

ISBN : 9783540413974

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Book Description

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.



Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

Author : L. Molnár

Publisher : Springer

Page : 243 pages

File Size : 46,75 MB

Release : 2006-11-15

Category : Mathematics

ISBN : 3540399461

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Book Description

The territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.



Stable Approximate Evaluation of Unbounded Operators

Author : C. W. Groetsch

Publisher : Springer Science & Business Media

Page : 134 pages

File Size : 45,27 MB

Release : 2007

Category : Mathematics

ISBN : 3540399429

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Book Description

Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.



Introduction to Symplectic Dirac Operators

Author : Katharina Habermann

Publisher : Springer

Page : 131 pages

File Size : 40,95 MB

Release : 2006-10-28

Category : Mathematics

ISBN : 3540334211

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Book Description

This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.



The Method of Approximate Inverse: Theory and Applications

Author : Thomas Schuster

Publisher : Springer

Page : 193 pages

File Size : 35,19 MB

Release : 2007-04-26

Category : Mathematics

ISBN : 3540712275

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Book Description

This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.



Transseries and Real Differential Algebra

Author : Joris van der Hoeven

Publisher : Springer

Page : 265 pages

File Size : 15,29 MB

Release : 2006-10-31

Category : Mathematics

ISBN : 354035591X

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Book Description

Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.