Functional Analysis: Fundamentals
Linear and continuous transformations, principle of uniform Banach-Steinhaus limitation, open application theorem, closed graph theorem. Duality, dual space, reflective spaces, adjunct operator and self-adjunct. Weak topologies, weak and weak* convergence, Banach-Alaoglu theorem. Spectrum of operators, compact operators, normal operators. Spectral theorem for limited self-adjunct and normal operators.
· Bachman, Narici (2000). Functional Analysis. Dover.
· W. Rudin. Functional analysis. McGraw-Hill, New York, 1973
· H. Brezis. Functional analysis, Sobolev spaces and partial differential equations. Springer Science & Business Media, 2010
· Friedman (1982). Foundations of Modern Analysis. Dover.
· Oliveira (2015). Introdução à Análise Funcional. IMPA.
· F. Clarke. Functional analysis, calculus of variations and optimal control, volume 264. Springer, 2013
· J.B. Conway. A course in functional analysis, volume 96. Springer Science & Business Media, 2013
· N. Dunford and J.T. Schwartz. Linear operators part I: general theory, volume 7. Interscience publishers New York, 1958