Álgebras de
Operadores / Operator Algebras
General results for Banach algebras: Spectrum and spectral radius. The Gelfand representation theory for commutative Banach algebras. Functional calculus. Spectral theorem. C* Algebras: The Gelfand Naimark theorem (commutative algebras). The functional calculus for normal operators. Positive elements. Positive linear functionals. States and pure states. The Gelfand-Naimark-Segal construction. The Gelfand-Naimark theorem. Von Neumann algebras. Double commutant theorem. Kaplansky density theorem. Liminal and postliminal C* algebras. Crossed products. The isomorphism theorem for commutative groups and algebras. Local-trajectory method. Representations of Banach algebras: Primitive ideals. Primitive algebras. Irreducible representations. The Jacobson radical. The Jacobson topology. Representations of algebras that satisfy a polynomial identity. Algebras generated by two idempotents. The Allan-Douglas localization principle and Representation Theory.
Teacher PAULO R. PINTO