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.


TP 13

12 Dezembro 2024, 10:30 Maria Teresa Faria da Paz Pereira

Continuation of Lecture 25.