A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Basic Classes of Linear Operators
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Editorial Reviews
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"With a name like Gohberg–Goldberg–Kaashoek, it has got to be good. But let me count the ways. If you are interested in learning the basic theories of Hilbert and Banach spaces together with the well-known operators that act on them, this book is for you. It is intended for advanced undergraduate and beginning graduate students in mathematics.... The volume is actually a second edition of Basic Operator Theory by Gohberg and Goldberg.... Exercises and examples have been added.... The text is well written, clear, and readable.... A student at the specified level will have no difficulty understanding the presentation." —SIAM Review "The material is presented in a very clear way, emphasizing concepts over technical generalities. Another pleasant feature of the book is the large number of examples and exercises. In summary, the authors have successfully found an interesting way from the elementary level to some of the highlights of operator theory." - Monatshefte für Mathematik
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Inside This Book
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First Sentence:
Let C denote the set of complex numbers and let H = C be the set of all n-tuples (E1.....En) of complex numbers with addition and scalar multiplication defined as follows. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
section method converges, finite section method, compact positive operator, straightforward computation verifies, compact self adjoint operator, right invertible, left invertible, standard orthonormal basis, new scalar product, lim det, closed graph theorem, invertible operator, finite rank, winding number, closed unit disc, function det, compact operator, including infinity, bounded linear operator, continuous complex valued function, graph norm, spectral theorem, singular integral operators New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let C denote the set of complex numbers and let H = C be the set of all n-tuples (E1.....En) of complex numbers with addition and scalar multiplication defined as follows. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
section method converges, finite section method, compact positive operator, straightforward computation verifies, compact self adjoint operator, right invertible, left invertible, standard orthonormal basis, new scalar product, lim det, closed graph theorem, invertible operator, finite rank, winding number, closed unit disc, function det, compact operator, including infinity, bounded linear operator, continuous complex valued function, graph norm, spectral theorem, singular integral operators 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 21
books:
See all 21 books this book cites
1
book
cites this book:
- Linear Operators, Part 1: General Theory (Pure and Applied Mathematics, Vol. 7) by Nelson Dunford in Back Matter (1), and Back Matter (2)
- Introduction to Functional Analysis by Angus E. Taylor in Back Matter (1), and Back Matter (2)
- Classes of Linear Operators Vol. 2 (Operator Theory: Advances and Applications) (v. 2) by Israel Gohberg in Front Matter, and Back Matter
- Linear Operators in Hilbert Spaces (Graduate Texts in Mathematics) by Joachim Weidmann in Back Matter
- The Madison Colloquium (Colloquium Publications) by Leonard Eugene Dickson and William Fogg Osgood in Back Matter
See all 21 books this book cites
- Indefinite Linear Algebra and Applications by Israel Gohberg in Back Matter
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