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Editorial Reviews
Review
"This is an interesting, useful and informative work, well worth the effort required to deal with its many results." R.H. Cox, Mathematical Reviews
"A useful well-written guide." The American Mathematical Monthly
Product Description
This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis, function theory, orthogonal series, and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness, and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex, and real analysis. As the only introduction to the modern theory of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.
See all Editorial Reviews
"This is an interesting, useful and informative work, well worth the effort required to deal with its many results." R.H. Cox, Mathematical Reviews
"A useful well-written guide." The American Mathematical Monthly
Product Description
This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis, function theory, orthogonal series, and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness, and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex, and real analysis. As the only introduction to the modern theory of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.
See all Editorial Reviews
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Inside This Book
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First Sentence:
This introductory part contains background material. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
bounded extension property, rich subspace, basic sequence equivalent, partial sum projection, disc algebra, bounded approximation property, summing operators, unit vector basis, ball algebra, biorthogonal functionals, series unconditionally convergent, sublinear operator, unconditionally convergent series, local reflexivity, complemented subspace, continuum cardinality, reflexive subspaces, interpolating sequence, unconditional basis, absolutely summing, homogenous polynomials, uniform algebra, operator ideal, probability measure space, isomorphic embedding Key Phrases - Capitalized Phrases (CAPs): (learn more)
Absolutely Summing And Related Operators, Weak Topologies, Applying Proposition, Applying Theorem, Proof of Lemma, Using Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This introductory part contains background material. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
bounded extension property, rich subspace, basic sequence equivalent, partial sum projection, disc algebra, bounded approximation property, summing operators, unit vector basis, ball algebra, biorthogonal functionals, series unconditionally convergent, sublinear operator, unconditionally convergent series, local reflexivity, complemented subspace, continuum cardinality, reflexive subspaces, interpolating sequence, unconditional basis, absolutely summing, homogenous polynomials, uniform algebra, operator ideal, probability measure space, isomorphic embedding Key Phrases - Capitalized Phrases (CAPs): (learn more)
Absolutely Summing And Related Operators, Weak Topologies, Applying Proposition, Applying Theorem, Proof of Lemma, Using Lemma 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)
10
books
cite this book:
See all 10 books citing this book
- Absolutely Summing Operators (Cambridge Studies in Advanced Mathematics) by Joe Diestel in Front Matter, and Back Matter
- Köthe-Bochner Function Spaces (Progress in Mathematics) by Pei-Kee Lin on page 100, and page 218
- The Functional Calculus for Sectorial Operators (Operator Theory: Advances and Applications) by Markus Haase in Back Matter
- Stochastic Processes and Functional Analysis (Lecture Notes in Pure and Applied Mathematics) by Jerome Goldstein on page 218
- An Introduction to Nonharmonic Fourier Series (v. 93) by Robert M. Young in Back Matter
See all 10 books citing this book
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