The aim of this course is to provide a solid foundation in functional analysis. The content includes linear operators and, in particular, linear functionals, in linear normed and Banach spaces, and in Hilbert spaces. Besides the basic concepts the course will finally rest on the three corner stone theorems, viz., the Hahn-Banach theorem of Extension of bounded linear functional in linear normed spaces, the uniform boundedness principle (Banach-Steinhaus Theorem) and the open mapping theorems (the closed range theorem).

CILO-1: Apply concepts and basic properties of Hilbert and Banach spaces to solve problems. CILO-2: Analyze the properties of linear functionals, transformations, and operators in Hilbert and Banach spaces. CILO-3: Construct proofs of the Hahn-Banach theorem, the uniform boundedness principle (Banach-Steinhaus Theorem), and the open mapping theorem in functional analysis.