4 hours of lectures and exercises per week.
Lecturer:
Henrik Stetkær
Content:
We cite from the preface of the text book that we shall use in the course: ``The
material contained in this book falls under Kelley's label: What Every Young
Analyst Should Know." The course deals with the interplay between topological structures and vector space
structures as exemplified by Banach spaces and Hilbert spaces. It is an introduction
to functional analysis which is the study of topological vector spaces and linear
operators between them. We discuss general topology and apply it to weak topologies. Afterwards we prove
the three basic principles of functional analysis: The closed graph theorem, the
uniform bounded principle and the Hahn-Banach extension theorem. Furthermore
we give an introduction to the theory of Banach algebras.
Prerequisites:
Analysis 1.
Literature:
Gert K. Pedersen: Analysis Now, Springer-Verlag 1989.