Functional Analysis


Complete metric spaces. Fixed point theorem. Theorem of embedded balls. Baire theorem. Compactness: equivalent definitions. Arzela-Ascoli theorem. Normed linear spaces and applications: Banach spaces. Spaces of continuous linear applications. Dual space. Cauchy-Schwarz inequality. Parallelogram law. Orthogonalization. Hilbert spaces. Fourier series. Bessel's inequality. Parseval equality. Riesz-Fisher theorem. Hahn-Banach theorem. Minkowski function. Separation theorems. General form of linear functionals: functional in spaces of sequences; in Hilbert spaces. Riesz theorem. Weak convergence in a normed space and its dual. Banach-Steinhaus theorem. Compactness in the dual space. Topological vector spaces: Theorem of Kolmogorov. Weak topologies. Banach theorem of the inverse. Symmetric compact applications: Hilbert's Theorem. Fredholm theory.

Research and Events


  • PhD Defense
    Fernando Lucatelli Nunes - Pseudomonads and Descent
    10:00 - Sala dos Capelos, Univ. Coimbra
    January 24, 2018
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Defended Theses

  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
  • Representations of generalized quivers
      Artur Duarte Ferreira de Araújo (June 2017)
      Peter Gothen
  • On semisimple Hopf actions
      Deividi Ricardo Pansera (June 2017)
      Christian Edgar Lomp
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