Sumários
Lecture 12
20 Outubro 2025, 10:30 • Maria Teresa Faria da Paz Pereira
Point spectrum of bounded linear operators in L(E), for E normed space; examples.
Point spectrum of compact self-adjoint operators: main properties. Theorem of spectral decomposition of a compact self-adjoint operator.
Lecture 11
15 Outubro 2025, 11:00 • Maria Teresa Faria da Paz Pereira
Correction of the Assignment 2. Examples and problems about Hilbert spaces.
TP 5
13 Outubro 2025, 11:30 • Maria Teresa Faria da Paz Pereira
Continuation of Lecture 10: examples and exercices of compact and non compact linear bounded operators.
Lecture 10
13 Outubro 2025, 10:30 • Maria Teresa Faria da Paz Pereira
The approximation problem for compact operators in L(E,H) with E normed space and H Hilbert.
Examples of compact and non compact linear bounded operators.
Ascoli-Arzelà Theorem: statement and a proof. The Fredholm integral operators are compact in C([a,b]) with the norm of uniform convergence. The Fredholm integral operators are compact in L^2([a,b]).