Elementary Functional Analysis
Paperback
Series: de Gruyter Textbook
Publisher Price: $92.99
ISBN13: 9783110613919
Publisher: de Gruyter
Published: Oct 8 2018
Pages: 330
Weight: 1.17
Height: 0.69 Width: 6.69 Depth: 9.61
Language: English
While there is a plethora of excellent, but mostly tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constraints of the standard, for the United States, one-semester graduate curriculum (fifteen weeks with two seventy-five-minute lectures per week).
The book consists of seven chapters and an appendix taking the reader from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), through the basics of linear operators and functionals, the three fundamental principles (the Hahn-Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems) with their numerous profound implications and certain interesting applications, to the elements of the duality and reflexivity theory. Chapter 1 outlines some necessary preliminaries, while the Appendix gives a concise discourse on the celebrated Axiom of Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's Lemma, and Zermello's Well-Ordering Principle), and ordered sets.
Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. It contains 112 Problems, which are indispensable for understanding and moving forward. Many important statements are given as problems, a lot of these are frequently referred to and used in the main body. There are also 376 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in necessary details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problem and exercises being supplied with existential'' hints.
The book is generous on Examples and contains numerous Remarks accompanying every definition and virtually each statement to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential.
The prerequisites are set intentionally quite low, the students not being assumed to have taken graduate courses in real or complex analysis and general topology, to make the course accessible and attractive to a wider audience of STEM (science, technology, engineering, and mathematics) graduate students or advanced undergraduates with a solid background in calculus and linear algebra.
With proper attention given to applications, plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester graduate course on the fundamentals of functional analysis for students in mathematics, physics, computer science, and engineering.
Contents
Preliminaries
Metric Spaces
Normed Vector and Banach Spaces
Inner Product and Hilbert Spaces
Linear Operators and Functionals
Three Fundamental Principles of Linear Functional Analysis
Duality and Reflexivity
The Axiom of Choice and Equivalents
Also in
General Mathematics
Math Practice Workbook Grades 6-8: 1000+ Questions You Need to Kill in Middle School by Brain Hunter Prep
Brain Hunter Prep
Paperback
Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter
Orlin, Ben
Hardcover
The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics
Bardi, Jason Socrates
Hardcover
Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Sands, Matthew
Feynman, Richard P.
Leighton, Robert B.
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
Counting with - Contando Con Frida (Bilingual: English/Spanish): A Bilingual Counting Book
Stein, Ariana
Rodriguez, Patty
Hardcover
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Hardcover
Sudoku for Brain Fitness: 90-Day Challenge to Sharpen the Mind and Strengthen Cognitive Skills
Demyanovich, Julie
Clontz, Steven
Paperback
Vector: A Surprising Story of Space, Time, and Mathematical Transformation
Arianrhod, Robyn
Hardcover
The Art of Strategy: A Game Theorist's Guide to Success in Business and Life
Nalebuff, Barry J.
Dixit, Avinash K.
Paperback
50 Math Tricks That Will Change Your Life: Mentally Solve the Impossible in Seconds
Zakowich, Tanya
Paperback
Talentos Ocultos: La Genialidad No Tiene Color. La Fuerza No Tiene Género. El Valor No Tiene Límite.
Shetterly, Margot Lee
Paperback
The Indisputable Existence of Santa Claus: The Mathematics of Christmas
Evans, Thomas Oléron
Fry, Hannah
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
Who Gets What -- And Why: The New Economics of Matchmaking and Market Design
Roth, Alvin E.
Paperback
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
Oakley, Barbara
Paperback
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
Sutton, Daud
Lundy, Miranda
Ashton, Anthony
Hardcover
100 Days of Timed Tests, Multiplication, and Division Facts 1 to 12, Grade 3-5, Math Drills, Daily Practice Workbook
Abczbook Press
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
Touchthinklearn: Numbers: (Board Books for Baby Learners, Touch Feel Books for Children)
Deneux, Xavier
Hardcover
SAT Level Up! Math: 300+ Easy, Medium, and Hard Drill Questions for Scoring Success on the Digital SAT
The Princeton Review
Paperback
Sciencia: Mathematics, Physics, Chemistry, Biology, and Astronomy for All
Tweed, Matt
Watkins, Matthew
Betts, Moff
Hardcover
Un Elefante: Numbers / Números (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python
Raschka, Sebastian
Liu, Yuxi (Hayden)
Mirjalili, Vahid
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
Graph Paper Composition Notebook: Quad Ruled 5x5, Grid Paper for Students in Math and Science
Wizo, Math
Paperback
Do Plants Know Math?: Unwinding the Story of Plant Spirals, from Leonardo Da Vinci to Now
Golé, Christophe
Dumais, Jacques
Douady, Stéphane
Hardcover
The 125 Best Brain Teasers of All Time: A Mind-Blowing Challenge of Math, Logic, and Wordplay
Danesi, Marcel
Paperback
The Secret Lives of Numbers: A Hidden History of Math's Unsung Trailblazers
Revell, Timothy
Kitagawa, Kate
Hardcover
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Shermer, Michael
Benjamin, Arthur
Paperback
The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science
Schneider, Michael S.
Paperback
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everythingelse
Ellenberg, Jordan
Paperback
Concrete Mathematics: A Foundation for Computer Science
Graham, Ronald
Patashnik, Oren
Knuth, Donald
Hardcover
Theory of Games and Economic Behavior (Large Print Edition)
Neumann, John Von
Morgenstern, Oskar
Hardcover
Schaum's Outline of Mathematical Handbook of Formulas and Tables
Liu, John
Spiegel, Murray R.
Lipschutz, Seymour
Paperback
GED Math Test Tutor, for the 2025-2026 GED Test: All the Tools You Need to Succeed
Rush, Sandra
Paperback
Waves in an Impossible Sea: How Everyday Life Emerges from the Cosmic Ocean
Strassler, Matt
Hardcover
Exámenes Nacionales: XXV Onmapsb
Talamantes Román, Adrián
Ochoa Castillo, Orlando
Meré Hidalgo, Pablo
Paperback
Mastering Essential Math Skills, Book 2: Middle Grades/High School, 3rd Edition: 20 minutes a day to success
Fisher, Richard W.
Paperback
New York Post Fiendish Sudoku: The Official Utterly Addictive Number-Placing Puzzle
Gould, Wayne
Paperback
Mathematics of Machine Learning: Master linear algebra, calculus, and probability for machine learning
Danka, Tivadar
Paperback
HOW TO WIN MEGA MILLIONS LOTTERY JACKPOT ..How TO Increased Your odds by 71%: 2004 Pennsylvania Powerball Winner Tells LOTTERY&GAMBLING Secrets To Win
Secrets, Powerball Money
Paperback
To Mock a Mockingbird: And Other Logic Puzzles Including an Amazing Adventure in Combinatory Logic
Smullyan, Raymond M.
Paperback
Alan Turing: The Enigma: The Book That Inspired the Film the Imitation Game - Updated Edition
Hodges, Andrew
Paperback
New Art and Science of Teaching Mathematics: (Establish Effective Teaching Strategies in Mathematics Instruction)
Lang-Raad, Nathan D.
Marzano, Robert J.
Paperback
Serious Cryptography, 2nd Edition: A Practical Introduction to Modern Encryption
Aumasson, Jean-Philippe
Paperback
