A Course in Functional AnalysisSpringer New York, 1985 - 404 עמודים Functional 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. |
תוכן
Preface | 1 |
3 FiniteDimensional Normed Spaces | 3 |
4 Quotients and Products of Normed Spaces | 4 |
זכויות יוצרים | |
79 קטעים אחרים שאינם מוצגים
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
A₁ abelian assume B₁ ball Banach algebra Banach space Borel bounded linear C*-algebra closure Co(X compact normal operator compact operator compact subset continuous function continuous seminorm converges convex subset Corollary countable cyclic defined Definition denoted dense dim ker Example Exercise extreme point f₁ fact finite rank functional calculus functions f h in H h₁ h₂ Hence Hilbert space homeomorphism ideal identity implies invertible isometrically isomorphic isometry ker(A L²(µ Lemma linear functional linear manifold linear span linear subspace locally compact measure space metric normed space Note orthonormal P₁ polynomial PROOF ran(A reader reflexive result self-adjoint operator seminorm sequence space and let spectral measure Spectral Theorem statements are equivalent Suppose surjective unique unitary vector space Verify the statements weak topology weak-star weakly compact y₁