Topological Vector SpacesCUP Archive, 1980 - 172 oldal |
Tartalomjegyzék
The aim of this tract is to give an account of the theory of topo | 7 |
Preface page | 8 |
Duality and the HahnBanach theorem | 23 |
Topologies on dual spaces and the MackeyArens theorem | 44 |
Barrelled spaces and the BanachSteinhaus theorem | 65 |
Inductive and projective limits | 76 |
Completeness and the closed graph theorem | 101 |
Some further topics | 127 |
Compact linear mappings | 142 |
Appendix | 155 |
168 | |
Más kiadások - Összes megtekintése
Gyakori szavak és kifejezések
absolutely convex envelope absolutely convex neighbourhood absorbent algebraic applied Banach space barrelled barrelled space base of neighbourhoods bounded sets bounded subsets bourhood called Cauchy Chapter clearly closed absolutely convex closed graph closed vector subspace closure compact set contained continuous linear mapping convergence convex topology COROLLARY corresponding defined definition denoted direct sum dual pair elements equicontinuous equivalent example fact filter finer finite follows Fréchet space fully complete functions give given Hence identity intersection isomorphism Lemma meet metrisable nearly normed space origin polar precompact projective limit Proof Prop PROPOSITION prove quotient result satisfied scalar seminorms separated convex space sequence space E space F spanned strand strong Suppl supplement Suppose taking theorem topology of A-convergence topology of uniform uniform convergence union vector space vector subspace weakly