Sumários
Lecture 27
19 Dezembro 2024, 11:00 • Maria Teresa Faria da Paz Pereira
Continuation of last lecture.
TP 14
19 Dezembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira
Correction of assignment #6. Resolution of exercises of Chapter 3.
Lecture 26
16 Dezembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira
Weak-star convergence: properties of weak-star sequences.
Reflexive spaces. Reflexibility and separability. James' Theorem (without proof): applications. Alaoglu's Theorem. For E separable normed space, the weak-star topology in the unitary ball of E' is metrizable.
Resolution of exercises of Chapter II.
Lecture 25
12 Dezembro 2024, 11:00 • Maria Teresa Faria da Paz Pereira
Weak convergence on normed space: examples; properties of weakly convergent sequences.The open unitary ball of an infinitely dimensional normed space is not open for the weak topology; the convex sets are weakly closed iff they are strongly closed.
Definition of the weak-star topology in the dual.