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Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821849808
Category : Mathematics
Languages : en
Pages : 360
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Book Description
A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821849808
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 9780821849804
Category : Mathematics
Languages : en
Pages : 362
Get Book Here
Book Description
A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Author: Vladimir Kozlov
Publisher: American Mathematical Soc.
ISBN: 0821807544
Category : Mathematics
Languages : en
Pages : 426
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Book Description
For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Bob Coecke
Publisher: Springer Science & Business Media
ISBN: 9401712018
Category : Science
Languages : en
Pages : 329
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Book Description
The present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic.
Author: E. Pap
Publisher: Elsevier
ISBN: 0080533094
Category : Mathematics
Languages : en
Pages : 1633
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Book Description
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Author: P.A. Grillet
Publisher: Springer Science & Business Media
ISBN: 1475733895
Category : Mathematics
Languages : en
Pages : 443
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Book Description
This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.
Author: R. A. Bailey
Publisher: Cambridge University Press
ISBN: 1009465945
Category : Mathematics
Languages : en
Pages : 452
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Book Description
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821822349
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This paper is concerned with the structure of three interrelated classes of objects: partially ordered abelian groups with countable interpolation, [Hebrew]Aleph0-continuous regular rings, and finite Rickart C*-algebras. The connection from these rings and algebras to these groups is the Grothendieck group K0, which, for all [Hebrew]Aleph0-continuous regular rings and most finite Rickart C*-algebras, is a partially ordered abelian group with countable interpolation. Such partially ordered groups are shown to possess quite specific representations in spaces of affine continuous functions on Choquet simplices. The theme of this paper is to develop the structure theory of these groups and these representations, and to translate the results, via K0, into properties of [Hebrew]Aleph0-continuous regular rings and finite Rickart C*-algebras.
Author: Vincent F. Hendricks
Publisher: Springer Science & Business Media
ISBN: 9401735980
Category : Philosophy
Languages : en
Pages : 387
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Book Description
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Author: Jon Aaronson
Publisher: American Mathematical Soc.
ISBN: 0821804944
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
