Dual Spaces.

27 Outubro 2014, 18:30 • Fernando Manuel Rodrigues Ferreira Gonçalves

Dual Spaces: Hahn-Banach Theorem; The second dual space; Alignment and orthogonal complements; Weak convergence.

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Dual Spaces.

20 Outubro 2014, 18:30 • Fernando Manuel Rodrigues Ferreira Gonçalves

Dual Spaces: Linear functionals.

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Further Topics on Normed Spaces. Hilbert Spaces.

13 Outubro 2014, 18:30 • Fernando Manuel Rodrigues Ferreira Gonçalves

Further Topics on Normed Spaces: Weierstrass theorem; Quotient spaces; Denseness and separability.

Hilbert Spaces: Inner product spaces; Orthogonality; Fourier series.

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Topological vector spaces.

8 Outubro 2014, 18:00 • Fernando Manuel Rodrigues Ferreira Gonçalves

Topological vector spaces; Preliminaries; Topological spaces; Metric spaces; Topological vector spaces; Normed linear spaces; Banach spaces.

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Vector spaces.

22 Setembro 2014, 18:30 • Fernando Manuel Rodrigues Ferreira Gonçalves

Vector spaces: Definition; Subspaces, linear combinations, and linear varieties; Convexity and cones; Linear independence and dimension.

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