Lectures and Exercises on Functional AnalysisAmerican Mathematical Soc. - 468 The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces. |
Spis treści
| 1 | |
4 Isomorphisms The problem of classification of objects | 25 |
5 Other classes of morphisms | 32 |
7 Functors | 45 |
Normed Spaces and Bounded Operators | 55 |
2 Inner products and nearHilbert spaces | 66 |
First acquaintance examples | 76 |
4 Topological and categorical properties of bounded operators | 82 |
7 Invitation to quantum functional analysis | 113 |
Banach Spaces and Their Advantages | 125 |
From Compact Spaces to Fredholm Operators | 191 |
Polynormed Spaces Weak Topologies and Generalized | 245 |
At the Gates of Spectral Theory | 297 |
Hilbert Adjoint Operators and the Spectral Theorem | 327 |
Fourier Transform | 413 |
| 455 | |
5 Some types of operators and operator constructions Projections | 93 |
6 Functionals and the HahnBanach theorem | 100 |
| 461 | |
Inne wydania - Wyświetl wszystko
Lectures and Exercises on Functional Analysis Александр Яковлевич Хелемский Podgląd niedostępny - 2006 |
Kluczowe wyrazy i wyrażenia
adjoint operator arbitrary Banach algebra Banach space bijection bilinear Borel bounded operator C*-algebras calculus called classical coincides commutative compact operator complete consider contraction operator convergence coproduct Corollary corresponding countable defined Definition denoted dense diagram element epimorphism Example Exercise exists fact family of prenorms finite finite-dimensional Fourier transform Fredholm operator functional analysis functional ƒ functor Hausdorff Hence Hilbert spaces Hint homomorphism Im(S implies injective integral interval inverse isometric isomorphism Ker(S lemma linear operator linear space locally compact mapping mathematical metric space morphisms non-zero normed space notion numbers objects obviously operator acting orthogonal orthonormal polynormed space prenormed space Proof properties Proposition quantum space reader respect rest is clear Section selfadjoint selfadjoint operator sequence spectrum subset subspace Suppose surjective tensor product theory topological isomorphism topological space totally bounded unique unitarily unitary equivalence vector zero