LFU:online

Students who have completed the course have
understood the content of the lectures and are able to reproduce and to apply it. They are able to acquire similar contents independently.

This is a (slightly) advanced course on functional analysis. Based on the Analysis courses in the Bachelor programme, the course aims at providing a solid foundation on more advanced by still somewhat fundamental concepts of functional analysis. We will focus on topics that have wide applications in various areas of mathematics.

We intend to cover the following topics:

• Weak topologies
• Schauder bases
• Structure of Banach spaces
• geometric properties of Banach spaces
• fixed point theory for nonexpansive mappings
• spectral theory for unbounded operators on Hilbert spaces

Continuous assessment (based on regular written and/or oral contribution by participants).

Course examination according to § 7, statute section on "study-law regulations"

• Bowers and Kalton: An introductory course in functional analysis. Springer, 2014.
• Albiac and Kalton: Topics in Banach space theory. Second edition. Springer, 2016.
• Fabian, Habala, Hájek, Montesinos, and Zizler: Banach space theory. The basis for linear and nonlinear analysis. Springer, 2011.
• Carothers: A Short Course on Banach Space Theory. Cambridge University Press, 2004.
• Goebel and Reich: Uniform Convexity, Hyperbolic Geometry, And Nonexpansive Mappings. Marcel Dekker, New York, 1984
• Schmüdgen: Unbounded Self-adjoint Operators on Hilbert Space. Springer, Dordrecht, 2012
• Birman, and Solomjak: Spectral theory of selfadjoint operators in Hilbert space. D. Reidel Publishing Co., Dordrecht, 1987