MATE-4330 Análisis Funcional
Banach Spaces: Definitions and examples. Subspaces, linear transformations, quotient spaces. Duality: Hahn-Banach’s theorem. Banach-Steinhaus’ theorems, the Open Mapping and the Closed Graph theorems. Applications: Adjoint operators. Hilbert Spaces: Definitions and examples, orthogonality. Continuous operators: Operator convergence. Hermetian, normal and unitary operations. Orthogonal projections. Compact operators: Introduction to spectral theory.
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