Sign-In
Cart
A First Course in Functional Analysis
Hardcover
ISBN13: 9781041309857
Publisher: CRC Press
Published: Mar 2 2027
Pages: 368
Language: English
A First Course in Functional Analysis offers a rigorous and self-contained introduction to the basic language, methods, and theorems of functional analysis. Written for advanced undergraduate students, beginning graduate students, and instructors, the book develops the subject without assuming measure theory or the Lebesgue integral as prerequisites. This choice allows the essential ideas of the theory to be presented through vector spaces, normed spaces, Banach spaces, Hilbert spaces, and linear operators, while maintaining a gradual and conceptually coherent path through the material.
The book begins with algebraic foundations, including fields, valuations, vector spaces, Hamel bases, quotient spaces, convexity, linear operators, linear functionals, hyperplanes, and the algebraic Hahn-Banach theorem. It then develops normed and Banach spaces, completions, finite-dimensional normed spaces, the Baire theorem, Schauder bases, separability, bounded linear operators, the Hahn-Banach theorem in normed spaces, duality, reflexivity, adjoint operators, and the fundamental theorems of functional analysis. Weak and weak-star convergence are treated from a sequential point of view. The final chapters present Hilbert space theory, compact operators, the Arzela-Ascoli theorem, integral operators, spectral theory, and the spectral theorem for compact self-adjoint operators. An appendix develops bounded variation and the Riemann-Stieltjes integral as tools for the representation of the dual of C([a, b]).
Key Features Include:
- A self-contained first course requiring no prior measure theory
- A gradual transition from algebraic foundations to operator theory
- Careful treatment of Hahn-Banach, duality, reflexivity, and the fundamental theorems
- A sequential approach to weak and weak-star convergence
- Exercises supporting both classroom use and independent study
The text is suitable for a first course and as a reference for readers seeking a precise foundation in modern analysis.
Also from
Aduén, Hugo
Also in
General Mathematics
The Golden Number: Pythagorean Rites and Rhythms in the Development of Western Civilization
Ghyka, Matila C.
Hardcover
How It All Works: All Scientific Laws and Phenomena Illustrated & Demonstrated
Dant, Adam
Clegg, Brian
Hardcover
Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Feynman, Richard P.
Leighton, Robert B.
Sands, Matthew
Paperback
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Hardcover
Math Practice Workbook Grades 6-8: 1000+ Questions You Need to Kill in Middle School by Brain Hunter Prep
Brain Hunter Prep
Paperback
The Art of Strategy: A Game Theorist's Guide to Success in Business and Life
Nalebuff, Barry J.
Dixit, Avinash K.
Paperback
WorkKeys Study Guide and Practice Test Questions: ACT WorkKeys Exam Prep and Review Book with Applied Mathematics, Locating Information, and Reading f
Trivium Exam Prep Team
Paperback
Who Gets What -- And Why: The New Economics of Matchmaking and Market Design
Roth, Alvin E.
Paperback
Tomoko Fuse's Amazing Kusudama Origami: Geometric Paper Art from Japan's Leading Expert!
Fuse, Tomoko
Paperback
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Hardcover
Mastering Essential Math Skills Book 2, Bilingual Edition - English/Spanish
Fisher, Richard W.
Paperback
Counting with - Contando Con Frida (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter
Orlin, Ben
Hardcover
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
50 Math Tricks That Will Change Your Life: Mentally Solve the Impossible in Seconds
Zakowich, Tanya
Paperback
The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics
Bardi, Jason Socrates
Hardcover
Touchthinklearn: Numbers: (Board Books for Baby Learners, Touch Feel Books for Children)
Deneux, Xavier
Hardcover
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
Sutton, Daud
Lundy, Miranda
Ashton, Anthony
Hardcover
Graph Paper Composition Notebook: Quad Ruled 5x5, Grid Paper for Students in Math and Science
Wizo, Math
Paperback
Vector: A Surprising Story of Space, Time, and Mathematical Transformation
Arianrhod, Robyn
Hardcover
Quantum Mechanics Done Right: The Shortest Path from Novice to Researcher
Freericks, James K.
Hardcover
Un Elefante: Numbers / Números (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
Oakley, Barbara
Paperback
New York Post Fiendish Sudoku: The Official Utterly Addictive Number-Placing Puzzle
Gould, Wayne
Paperback
ALEKS Math Placement Test Prep 2026: 1200 Verified Practice Questions with Accurate Answer Keys, Step-by-Step Worked Solutions, and Clear Concept Expl
Publishing, Kettford
Reid, Marcus L.
Paperback
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Benjamin, Arthur
Shermer, Michael
Paperback
Partial Differential Equations: Theory and Completely Solved Problems
Van Roessel, H.
Hillen, T.
Leonard, I. E.
Paperback
Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning
Liljedahl, Peter
Paperback
Concrete Mathematics: A Foundation for Computer Science
Knuth, Donald
Graham, Ronald
Patashnik, Oren
Hardcover
180 Days(r) Math for First Grade: Practice, Assess, Diagnose
Smith, Jodene
Smith, Jodene Lynn
Paperback
Number Systems and the Foundations of Analysis
Mathematics
Mendelson, Elliott
Dudley, Underwood
Paperback
Sudoku for Brain Fitness: 90-Day Challenge to Sharpen the Mind and Strengthen Cognitive Skills
Demyanovich, Julie
Clontz, Steven
Paperback
Math Fundamentals 3 - Geometry: For Middle School - A Quickstudy Laminated Reference Guide
Warren, Peggy
Wright, Susan
Expolog
Other
Talentos Ocultos: La Genialidad No Tiene Color. La Fuerza No Tiene Género. El Valor No Tiene Límite.
Shetterly, Margot Lee
Paperback
It's All a Game: The History of Board Games from Monopoly to Settlers of Catan
Donovan, Tristan
Paperback
Reaching for the Extreme: How the Quest for the Biggest, Fewest, and Weirdest Makes Math
Stewart, Ian
Hardcover
Cybernetics: Or the Control and Communication in the Animal and the Machine
Wiener, Norbert
Paperback
The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science
Schneider, Michael S.
Paperback
300 Math CrossWords: Addition, Subtraction, Multiplication, and Division Math CrossWords Grade 3 and Above, Age +8
Martin, Josh Ortiz
Paperback
Medical Dosage Calculations for Dummies
Snyder, Richard W.
Depuente, Vanessa
Schoenborn, Barry
Paperback
Make: Physics: Build Projects to Explore Calculus-Based Mechanics
Horvath, Joan
Cameron, Rich
Paperback