Feinstein, J. (Joel) (2008)
Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will in boundedness of operators, compactness and finite dimensionality; extension of functionals; sequence spaces and duality; as well as the basic properties of Banach algebras.
University of Nottingham