Sumários

Lecture 5

2 Outubro 2023, 10:30 • Maria Teresa Faria da Paz Pereira

The Riesz representation theorem; examples and consequences.

Hilbert basis: definition and examples. Separable (pre-)Hilbert spaces. Bessel inequality.

TP2

27 Setembro 2023, 11:30 • Maria Teresa Faria da Paz Pereira

Examples and exercises about normed spaces and bounded linear operators.

Lecture 4

27 Setembro 2023, 11:00 • Maria Teresa Faria da Paz Pereira

Orthogonal projection on complete sublinear spaces (cont). Decomposition of a Hilbert space as direct sum of a closed sublinear space and its orthogonal.

Lecture 3

25 Setembro 2023, 10:30 • Maria Teresa Faria da Paz Pereira

Revisions on normed spaces (cont.): the spaces l^p and L^p; examples of sub-spaces and bounded linear operators.

Linear spaces with an inner product and Hilbert spaces: general properties and examples. Projection on complete convex sets; orthogonal projection on complete sublinear spaces.

TP1

20 Setembro 2023, 11:30 • Maria Teresa Faria da Paz Pereira

Examples and exercises about normed spaces and bounded linear operators.