A Course in Functional AnalysisFunctional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts. |
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Contents
CHAPTER | 1 |
2 Orthogonality | 7 |
3 The Riesz Representation Theorem | 11 |
Copyright | |
98 other sections not shown
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Common terms and phrases
A₁ abelian application assume ball Banach algebra Banach space basis Borel bounded C*-algebra called Claim closed closure collection compact compact operator complete contains continuous function converges convex Corollary cyclic defined Definition denoted dense easy element equivalent Example Exercise extension fact finite functional calculus given gives h₁ Hence Hilbert space homomorphism ideal identity implies invariant invertible isometry isomorphism ker(A LČ(” Lemma linear functional manifold maximal measure measure space multiplication normal operator normed space Note polynomial positive preceding projection PROOF properties Proposition Prove reader reflexive representation result self-adjoint seminorm separable sequence shown spectral measure statements subset subspace Suppose symmetric Theorem theory topology transform unique unitary vector space Verify weak weakly
Bibliographic information
| Title | A Course in Functional Analysis Volume 96 of Graduate Texts in Mathematics, ISSN 0072-5285 Volume 96 of Lecture Notes in Statistics |
| Author | John B. Conway |
| Publisher | Springer New York, 1985 |
| Original from | the University of California |
| Digitized | Apr 6, 2011 |
| ISBN | 0387960422, 9780387960425 |
| Length | 404 pages |
| Subjects | › Mathematics / Calculus Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |