Sumários

TP 9

14 Novembro 2024, 11:00 • Maria Teresa Faria da Paz Pereira

Exercises about Chaper II, including some consequences of the Hahn-Banach Theorem.

Lecture 17

14 Novembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Hahn-Banach Thorem (real version): end of the proof. Hahn-Banach Theorem (complex version). Some important consequences of the Hahn-Banach Theorem.

Lecture 16

11 Novembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

A linear functional f in a normed space is continuos iff Ker f is closed. Counter-example. Zorn's Lemma (revision). Vector spaces of infinite dimension. Schauder bases for a normed space; examples.

Riesz's Lemma; consequences.

Hahn-Banach Theorem - real version (proof not yet complete).

Remark: This lecture had an extra time of 30 minutes (to compensate partially the lecture of Nov. 25th.

TP 8

7 Novembro 2024, 11:00 • Maria Teresa Faria da Paz Pereira

Correction of Assignment 3.

Resolution of exercises of Chapter II.

Lecture 15

7 Novembro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Quocient spaces E/M of normed spaces E and canonical map from E onto E/M: more properties.