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Course description: This course is an introduction to functional analysis. We will start with the basic theory of Hilbert and Banach spaces. We will then discuss topological vector spaces and weak topologies. In the second part of the class we will cover various fixed point theorems, compact operators, and the spectral theorem.
Resources : The topics covered in the class are contained in Chapters 1-4 from Essential results in functional analysis by R. Zimmer and Chapters 1-5 from A course in functional analysis by J.B. Conway.
Homework : There are three womework assignments: homework 1 , homework 2 and homework 3 . The homework is optional . However, you are strongly encouraged to attempt as many problems as possible and to turn in your work by the due dates.