Sumários
Lecture 22
4 Dezembro 2023, 10:30 • Maria Teresa Faria da Paz Pereira
The Principle of Uniform Boundedness. Corollaries and applications.
Duality between two vector spaces. Duality between a normed space E and its dual E'.
Examples of dual spaces for: a finite dimensional space; a Hilbert space; l^1: prove of the Riesz Representation Theorem for (l^1)'.
TP 10
29 Novembro 2023, 11:30 • Maria Teresa Faria da Paz Pereira
Correction of Assignment #4.
Resolution of problems for Chapter II
Lectue 21
29 Novembro 2023, 11:00 • Maria Teresa Faria da Paz Pereira
Continuation of the previous lecture.
Lecture 20
27 Novembro 2023, 10:30 • Maria Teresa Faria da Paz Pereira
Closed Graph Theorem (CGT). The graph-norm and an alternative proof of CGT. Examples and counter-examples.
Continuous projections and topological directs sums in a normed space. Examples of topological complementary spaces.
Sequences of operators in L(E,F) (E,F normed spaces): examples of pointwise convergence and norm convergence.
TP9
22 Novembro 2023, 11:30 • Maria Teresa Faria da Paz Pereira
(Used to complete the lecture.)
Open Mapping Theorem (end of the proof).
(Couter)example of application.