Sumários
Lecture 16
3 Novembro 2025, 10:30 • Maria Teresa Faria da Paz Pereira
Riesz's Lemma; consequences.
Hahn-Banach Theorem - real version.
Lecture 15
29 Outubro 2025, 11:00 • Maria Teresa Faria da Paz Pereira
Exercises and results about compact linear operators and compact self-adjoint linear operators.
Lecture 14
27 Outubro 2025, 10:30 • Maria Teresa Faria da Paz Pereira
Quotient spaces E/M, for E a normed space and M a closed linear
subspace: the canonical map
and its properties. More properties of quotient spaces, The space c of l^\infty is closed.
Linear hyperplanes, and their relation with linear functionals. A linear functional f in a normed space is continuous iff Ker f is closed. Counter-example.
Zorn's Lemma (revision). Vector spaces of infinite dimension. Schauder bases for a normed space; examples
Lecture 13
22 Outubro 2025, 11:00 • Maria Teresa Faria da Paz Pereira
Theorem of spectral decomposition of a compact self-adjoint operator (continuation of the proof) and corollaries.
Normed and Banach spaces: examples. Quotient spaces E/M, for E a normed space and M a closed linear subspace: definition; norm in E/M; first properties.