This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. <P>The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. <P>The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis.
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"This is a gentle introduction to functional analysis that is clearly written and comes with detailed, elegant and effective proofs and well-chosen examples. ... This book is written with great care and with much sympathy to the reader. It is pleasant to read... It is simply a good book to learn the foundations of functional analysis." ---- Zentralblatt MATH
"Each chapter includes exercises, in total 195 of the them, all provided with solutions at the end of the book. The text is as self-contained as possible... The authors have taken special care to be brief and not to overload the students with the enormous amount of information available on the subject." ---- EMS Newsletter
"Each chapter includes exercises, in total 195 of the them, all provided with solutions at the end of the book. The text is as self-contained as possible... The authors have taken special care to be brief and not to overload the students with the enormous amount of information available on the subject." ---- EMS Newsletter
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0 of 3 people found the following review helpful:
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good book,
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This review is from: Functional Analysis: An Introduction (Graduate Studies in Mathematics) (Hardcover)
This book is very good. It is well organized, gives the solutions to problems, well written with all basic facts.
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Great Condition Poor Choice of Text,
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This review is from: Functional Analysis: An Introduction (Graduate Studies in Mathematics) (Hardcover)
Delivered fine. Great condition and delivered well on time. Wish my professor wasn't using this text, however. Not the best handling of the material that I've seen so far.
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In this course we study linear spaces E over the field of real or complex numbers R or C. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed graph operator, closed symmetric operator, spectral family, multiplicative functional, boundary value conditions, complete normed space, spectral integral, residual spectrum, extremal points, compact operator, closed graph theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use Exercise, Ilxll Ilyll New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this course we study linear spaces E over the field of real or complex numbers R or C. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed graph operator, closed symmetric operator, spectral family, multiplicative functional, boundary value conditions, complete normed space, spectral integral, residual spectrum, extremal points, compact operator, closed graph theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use Exercise, Ilxll Ilyll 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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