Normed Linear Spaces |
Contents
| 1 | |
Normed Linear spaces | 24 |
Completeness compactness and reflexivity | 44 |
Unconditional convergence and bases | 58 |
Compact convex sets and continuous function spaces | 77 |
Norm and order | 96 |
Metric geometry in normed spaces | 110 |
Readers guide | 121 |
| 132 | |
Other editions - View all
Common terms and phrases
A₁ AL)-space Amer b₁ Banach space boundedly complete c₁ Cauchy closed linear subspace closure co(S co(w completely regular conjugate space contains continuous functions convergent convex hull convex set Corollary countable defined Definition element equivalent exists extreme points f₁ factor space finite subset finite-dimensional Hahn-Banach theorem Hausdorff space Hence homeomorphic hyperplane implies inner-product space interior point isometry isomorphic L₁ Lemma linear function linear isometry linear subspace linear topological space linearly independent locally convex mapping Math maximal metric space minimal facet monotone N₁ non-empty normed linear space normed space Proof properties prove reflexive rotund S₁ satisfies sequence set of extreme shows sublinear sublinear functional symmetric t₁ topological space topology totally bounded U₁ unit ball vector lattice w-compact w*-closed w*-topology weakly wedge x₁ ηεω ίξω κεμ κεω ΠΕΔ