Title of the course: Topics on Hilbert spaces
Instructor: Prof. Dimitris Papathanasiou
Institution: Sabanci University
Dates: 22-28 July 2024
Prerequisites: Linear Algebra, basic topology, basic real and complex analysis.
Level: Advanced undergraduate
Abstract: Functional analysis is the study of function and sequence spaces as well as the operators between them. The class of spaces which is closest to the Euclidean spaces and hence to our geometric intuition is Hilbert spaces. However, this intuition, many times is not sufficient and we mention as such instance, the infamous “Invariant Subspace Problem” which remains open for Hilbert spaces. We will develop the basic theory of Hilbert spaces, see the main examples of such spaces related to real and complex analysis, and discuss sporadic interesting topics about them.
Language: English