In this chapter we survey the main theorems of functional analysis that deal with Banach spaces, including the Hahn–Banach, Baire Category, Uniform Boundedness, Open Mapping, and Closed Graph Theorems. References for additional information on this material (and sources for many of the proof that we give) include the texts by Conway [Con90], Folland [Fol99], and Rudin [Rud91].
KeywordsHilbert Space Banach Space Normed Space Weak Convergence Positive Operator
Unable to display preview. Download preview PDF.