Sumários
Lectute 24
9 Dezembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira
Chap. 3: Definition of duality. Duality between a normed space E and
its dual E'. Examples of dual spaces for: a finite dimensional space and a
Hilbert space.
Some Riesz Representation Theorems: the dual spaces of l^1 and l^p (1<p<infty), and L^p (1<=p<infty, for L^p without proof); definition and properties of bounded variation functions; the dual of C([a,b]) with the supremum norm (without proof). Examples of application.
Weak convergence and weak topology on normed spaces.
TP 12
5 Dezembro 2024, 11:00 • Maria Teresa Faria da Paz Pereira
Correction of assignment #5. Resolution of exercises of Chapter 2.
Lecture 23
5 Dezembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira
Corollaries and applications the Principle of Uniform Boundedness.
Lecture 22
2 Dezembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira
The graph-norm and an alternative proof of the Closed Graph Theorem (CGT). Consequences. Examples and counter-examples.
Continuous projections and topological directs sums in a normed space. Examples of topological complementary spaces. Sequences of operators in L(E,F) (E,F normed spaces): pointwise convergence and norm convergence. The Principle of Uniform Boundedness.