Sumários

Lecture 19

12 Novembro 2025, 11:00 • Maria Teresa Faria da Paz Pereira

Continuation of Lecture 18.
Correction of assignment #4. Exercises involving quotient spaces, Riesz' Lemma, Hahn-Banach Theorem.

TP9

10 Novembro 2025, 11:30 • Maria Teresa Faria da Paz Pereira

Continuation of Lecture 18. Applications of Hahn-Banach Theorem.

Lecture 18

10 Novembro 2025, 10:30 • Maria Teresa Faria da Paz Pereira

Affine hyperplanes. Hahn-Banach Theorem-1st and 2nd geometric versions. Example.
1st and 2nd Baire Category Theorem (1st one without proof).

Lecture 17

5 Novembro 2025, 11:00 • Maria Teresa Faria da Paz Pereira

Hahn-Banach Theorem (complex version). Some important consequences of the Hahn-Banach Theorem. The notation of bidual.

TP8

3 Novembro 2025, 11:30 • Maria Teresa Faria da Paz Pereira

Continuation of Lecture 16.
Exercises about spectral decomposition of self-adjoint compact operators in Hilbert spaces.