This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS
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Second Edition J.B. Conway A Course in Functional Analysis "This book is an excellent text for a first graduate course in functional analysis . . . Many interesting and important applications are included . . . This book is a fine piece of work. It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." —MATHEMATICAL REVIEWS
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Most Helpful Customer Reviews
24 of 25 people found the following review helpful:
5.0 out of 5 stars
A Course in Functional Analysis ... the title is correct!,
By
This review is from: A Course in Functional Analysis (Hardcover)
I learned functional analysis by studying this book. I did this under the direction of a master teacher, John Erdman, who taught via a modified Moore Method. I found this very inspirational and challenging. BEFORE I took the course, I did not enjoy browsing the book, BUT I learned that the book, upon combination with the right amount of focus and effort, did a remarkable job of bringing functional analysis alive ... of transmiting the real essence to young, "sprouting" mathematicians. There is also an informality that brings a freshness to the book ... and this in a subject that could easily be studied without encountering this important ingredient in a mathematician's training.This book has as it's high point and goal the spectral theorem for normal operators. I add this because no one book can be all encompassing. If this and the spectral theorem goal are kept in mind, the omissions and emphasis found in the book will be found to be completely natural. This book should be in the library of anyone teaching functional analysis or who wants a working mathematician's masterfully developed course on functional analysis (with an eye to the spectral theorem for normal operators).
17 of 21 people found the following review helpful:
5.0 out of 5 stars
An Excellent Book !,
By Ami (Holon, Israel) - See all my reviews
This review is from: A Course in Functional Analysis (Hardcover)
This book is just excellent. The author decides to do something a little unusual, and starts talking about "Hilbert Spaces" before talking about "Banach Spaces". Conway writes down the matereal in a great way. He gives proves to almost every proposition, and gives lots of EXAMPLES and EXCERCISES (which are not given in most of the books about this subject). It's a good book for people who have never read this book before, as well as people who are currently studying the course. Also, conway extends the book's content by writing about advanced subjects (that are not studied in a first course about the subject), like locally convex spaces, weak topologies and even unbounded operators.
7 of 10 people found the following review helpful:
4.0 out of 5 stars
A wonderful first course for enthousiasts,
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This review is from: A Course in Functional Analysis (Hardcover)
The only reason for 4 stars instead of 5 is that I am not a great fan of Conway's style, and have wasted too much time on mangled examples in his Complex Analysis.That said, the layout here is superb, and the choice of topics just what is needed to get one of the ground. Beginners will find it useful to have a copy of Kreyszig at hand.
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Inside This Book
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First Sentence:
A Hilbert space is the abstraction of the finite-dimensional Euclidean spaces of geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
right modular unit, compact normal operator, closed symmetric extension, positively oriented system, closed symmetric operator, continuous one parameter unitary group, compactly supported measure, modular ideal, separating vector, show that the following statements, pairwise orthogonal projections, maximal ideal space, diagonalizable operator, normal operators, continuous seminorm, strict inductive limit, reducing subspace, ordered vector space, unilateral shift, surjective isometry, spectral measure, spectral theorem, sublinear functional, linear manifold, nonzero homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Hahn-Banach Theorem, Alaoglu's Theorem, Krein-Smulian Theorem, Riesz Representation Theorem, Riesz Functional Calculus, Zorn's Lemma, Lebesgue Dominated Convergence Theorem, Closed Graph Theorem, Stone-Weierstrass Theorem, Baire Category Theorem, Inverse Mapping Theorem, Prove Theorem, Radon-Nikodym Theorem, Principle of Uniform Boundedness, Prove Corollary, Stone's Theorem, Fredholm Alternative, Cauchy's Theorem, Lomonosov's Theorem, Parseval's Identity, Cauchy's Integral Formula, Dependence of the Spectrum, Schauder's Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A Hilbert space is the abstraction of the finite-dimensional Euclidean spaces of geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
right modular unit, compact normal operator, closed symmetric extension, positively oriented system, closed symmetric operator, continuous one parameter unitary group, compactly supported measure, modular ideal, separating vector, show that the following statements, pairwise orthogonal projections, maximal ideal space, diagonalizable operator, normal operators, continuous seminorm, strict inductive limit, reducing subspace, ordered vector space, unilateral shift, surjective isometry, spectral measure, spectral theorem, sublinear functional, linear manifold, nonzero homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Hahn-Banach Theorem, Alaoglu's Theorem, Krein-Smulian Theorem, Riesz Representation Theorem, Riesz Functional Calculus, Zorn's Lemma, Lebesgue Dominated Convergence Theorem, Closed Graph Theorem, Stone-Weierstrass Theorem, Baire Category Theorem, Inverse Mapping Theorem, Prove Theorem, Radon-Nikodym Theorem, Principle of Uniform Boundedness, Prove Corollary, Stone's Theorem, Fredholm Alternative, Cauchy's Theorem, Lomonosov's Theorem, Parseval's Identity, Cauchy's Integral Formula, Dependence of the Spectrum, Schauder's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter (1), and Back Matter (2)
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Front Matter, and Back Matter
- General Topology (Graduate Texts in Mathematics) by John L. Kelley in Front Matter, and Back Matter
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, and Back Matter
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- Recent Advances in Operator Theory and Related Topics: The Bela Szökefalvi-Nagy Memorial Volume (Operator Theory: Advances and Applications) by Laszlo Kerchy on page 170, and page 421
- One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) by Klaus-Jochen Engel in Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable II (Graduate Texts in Mathematics) (Pt. 2) by John B. Conway in Back Matter (1), and Back Matter (2)
- Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud in Back Matter
- Recent Advances in Operator Theory and Its Applications: The Israel Gohberg Anniversary Volume (Operator Theory: Advances and Applications) by Marinus A. Kaashoek on page 43
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