This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.
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"The book is very well written and the level is appropriate for the intended audience...It is easy to read and covers many interesting topics...a useful resource for basic and standard normed linear space theory...an excellent text." Mathematical Reviews
Book Description
This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
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Inside This Book
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First Sentence:
Everyday Euclidean space which underlies most of our mathematical activity, possesses some remarkable abstract structures which provide a rewarding study in their own right. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuous finite rank operators, unital normed algebra, consider the normed linear space, continuous projection operator, complex normed linear space, proper closed linear subspace, dimensional normed linear space, compact normal operators, positive hermitian form, maximal orthonormal set, nonmed linear space, normed linear spaces, basis fen, linear space structure, same scalar field, topological isomorphism, conjugate mapping, continuous linear mappings, real linear subspace, isometric isomorphism, proper linear subspace, pointwise bounded, orthogonal coefficients, closed unit ball, dense linear subspace Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hahn-Banach Theorem, Open Mapping Theorem, Uniform Boundedness Theorem, Riesz Representation Theorem, Closed Graph Theorem, Baire Category Theory, Bishop-Phelps Theorem, Cantor's Ternary Set, Consider the Banach, Mathematical Analysis, Riesz Theorem, Zorn's Lemma, Approximation Theorem, Baire's Theorem, Riesz Lemma, Acta Math, Dan Amir, London Math, Per Enflo, Schauder's Theorem, Stefan Banach, The Hahn-Barach Theorem, Zom's Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Everyday Euclidean space which underlies most of our mathematical activity, possesses some remarkable abstract structures which provide a rewarding study in their own right. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuous finite rank operators, unital normed algebra, consider the normed linear space, continuous projection operator, complex normed linear space, proper closed linear subspace, dimensional normed linear space, compact normal operators, positive hermitian form, maximal orthonormal set, nonmed linear space, normed linear spaces, basis fen, linear space structure, same scalar field, topological isomorphism, conjugate mapping, continuous linear mappings, real linear subspace, isometric isomorphism, proper linear subspace, pointwise bounded, orthogonal coefficients, closed unit ball, dense linear subspace Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hahn-Banach Theorem, Open Mapping Theorem, Uniform Boundedness Theorem, Riesz Representation Theorem, Closed Graph Theorem, Baire Category Theory, Bishop-Phelps Theorem, Cantor's Ternary Set, Consider the Banach, Mathematical Analysis, Riesz Theorem, Zorn's Lemma, Approximation Theorem, Baire's Theorem, Riesz Lemma, Acta Math, Dan Amir, London Math, Per Enflo, Schauder's Theorem, Stefan Banach, The Hahn-Barach Theorem, Zom's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 13
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6
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- Functional Analysis (Dover Books on Mathematics) by George Bachman in Front Matter, and page 249
- Functional Analysis by Walter Rudin in Front Matter, and page 249
- Introduction to the Analysis of Metric Spaces (Australian Mathematical Society Lecture Series) by John R. Giles in Front Matter
- Low Rank Representations and Graphs for Sporadic Groups (Australian Mathematical Society Lecture Series) by Cheryl E. Praeger in Front Matter
- An Introduction to Mathematical Physiology and Biology (Cambridge Studies in Mathematical Biology) by J. Mazumdar in Front Matter
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- Geometric Approaches to Differential Equations (Australian Mathematical Society Lecture Series) by Peter J. Vassiliou in Front Matter
- A Course in Modern Analysis and its Applications (Australian Mathematical Society Lecture Series) by Graeme L. Cohen in Front Matter
- Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter (Australian Mathematical Society Lecture Series) by Glenn R. Fulford in Front Matter
- Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) by John Banks in Front Matter
- Quantum Groups: A Path to Current Algebra (Australian Mathematical Society Lecture Series) by Ross Street in Front Matter
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