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Locally Convex Spaces

Author: M. Scott Osborne
Publisher: Springer Science & Business Media
ISBN: 3319020455
Size: 27.13 MB
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For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.

Topological Vector Spaces

Author: H.H. Schaefer
Publisher: Springer Science & Business Media
ISBN: 1461214688
Size: 79.35 MB
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Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras.

Locally Convex Spaces

Author:
Publisher: Springer Science & Business Media
ISBN: 3322905594
Size: 16.87 MB
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The present book grew out of several courses which I have taught at the University of Zürich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G. Garnir-M. De Wilde-J. Schmets [1], AGrothendieck [13], H. Heuser [1], J. Horvath [1], J.L. Kelley-I. Namioka et al. [1], G. Köthe [7], [10], A P. Robertson W. Robertson [1], W. Rudin [2], H.H. Schaefer [1], F. Treves [l], A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections. Chapters, sections, and the statements therein are enumerated in consecutive fashion.

A Primer On Hilbert Space Theory

Author: Carlo Alabiso
Publisher: Springer
ISBN: 3319037137
Size: 43.19 MB
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This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Foundations Of Complex Analysis In Non Locally Convex Spaces

Author: A. Bayoumi
Publisher: Elsevier
ISBN: 9780080531922
Size: 59.58 MB
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All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory. Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material. The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem. Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions. The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one. The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems. bull; The book contains new generalized versions of: i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others. ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author. bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995. bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

A Course In Functional Analysis

Author: John B. Conway
Publisher: Springer Science & Business Media
ISBN: 1475738285
Size: 25.23 MB
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Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

Modern Methods In Topological Vector Spaces

Author: Albert Wilansky
Publisher: Courier Corporation
ISBN: 0486493539
Size: 39.58 MB
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"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--

An Introduction To Banach Space Theory

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 1461206030
Size: 37.54 MB
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Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Locally Convex Spaces Over Non Archimedean Valued Fields

Author: C. Perez-Garcia
Publisher: Cambridge University Press
ISBN: 9780521192439
Size: 75.14 MB
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Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.