Sumários
Lecture 25
13 Dezembro 2023, 11:30 • Maria Teresa Faria da Paz Pereira
Weak convergence on normed space: examples; properties of weakly convergent sequences.
Weak-star convergence; reflexive spaces, statement of Alaoglu's Theorem.
TP 12
13 Dezembro 2023, 11:00 • Maria Teresa Faria da Paz Pereira
Examples and exercises for Chapter 3.
Lecture 24
11 Dezembro 2023, 10:30 • Maria Teresa Faria da Paz Pereira
Still some applications of main theorems from Chapter 2 (Closed Graph Theorem, PUB, completary spaces).
Riesz Representation Theorems for : l^p and L^p (1<p<infty), C([a,b]) with the supremum norm (without proofs). Examples of application.
Weak convergence and weak topology on normed space.
TP 11
6 Dezembro 2023, 11:00 • Maria Teresa Faria da Paz Pereira
Correction of assignment #5; resolution of exercises of Chapter 2.