Schauder bases and locally complemented subspaces of Banach spaces

2014

Masteroppgave i matematikkdidaktikk – Universitetet i Agder 2014 The thesis is about Schauder basis in infinite-dimensional Banach spaces and locally complemented subspaces. It starts with the notion of bases and it proves that it is equivalent with that of Schauder basis. It follows with some general theory about bases, and gives the notion of basic sequences and equivalence of bases. It proves that every Banach space has a basic sequence. Next it gives some general theory about unconditional basis. To give an other version of the definition of complemented subspaces, we present adjoint operators and projections. We prove that c0 is not complemented in l∞. The Principle of Local Reflexivit…