lecture 22

13 maio 2019, 14:00 • Helena Mascarenhas

Caracterization of the invertible elements on a Banach algebra in terms of its ideals, and also in terms of its linear multiplicative functionals. Gelfand -Mazur theorem. Applications to commutative Banach algebras.

lecture 21

9 maio 2019, 15:30 • Helena Mascarenhas

 Every Banach algebra can be embedded in a unital Banach algebra. Neumann´s series. The group of invertible elements is open. Three notions  of convergence: weak convergence, strong convergence and convergence in norm.

lecture 20

6 maio 2019, 14:00 • Helena Mascarenhas

Uniform boundedness principle. Banach-Steinhaus Theorem. 

Banach algebras. Examples.

lecture 19

2 maio 2019, 15:30 • Helena Mascarenhas

Adjoint operator and orthogonal space (or annihilator) in the context of normed spaces.

Open mapping theorem and  Bounded inverse theorem. Closed linear operators  and the closed graph Theorem.

lecture 18

29 abril 2019, 14:00 • Helena Mascarenhas

Complemented subspace. Schauder basis and its relation with separability property.  Reflexive spaces. Bidual space.