Sumários

Lecture 6

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

Hilbert bases for pre-Hilbert spaces; separable spaces. Examples of separable and non-separable Hilbert spaces. Bessel inequality. Fourier series relative to a Hilbert basis in Hilbert spaces and Parseval identity. Every separable, infinite dimensional Hilbert space is isomorphic and isometric to l^2.

Lecture 5

24 Setembro 2025, 11:00 • Maria Teresa Faria da Paz Pereira

Decomposition of a Hilbert space as direct sum of a closed sublinear space and its orthogonal.
The Riesz representation theorem; examples and consequences.
Hilbert bases on pre-Hilbert spaces: definition and examples.

TP 2

22 Setembro 2025, 11:30 • Maria Teresa Faria da Paz Pereira

Examples and exercises on the topics of the previous lectures.

Lecture 4

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

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

Lecture 3

17 Setembro 2025, 11:00 • Maria Teresa Faria da Paz Pereira

The subspaces c and c_0 of l^\infty.
More examples and exercises about normed spaces and bounded linear operators on normed spaces.