MATH 541-Functional Analysis
Time: MWF 12:00-12:50pm
Location: 347 Altgeld Hall
Junge Office hours: Thursday 5-6, Grader
Analysis, Math 541, is one of the jewel among the analysis
courses in our graduate school. In a nutshell one can say that
functional analysis is linear algebra in infinite dimension, with just
the right amount of topology to make it managable. The area of
functional analysis was born out of different fields such as
Banach spaces, operator algebra and ODE's discovering that a few
principlies are useful in all of them. I invite the participants in
this course to find out what is their favorite application.
I: Review of Banach space properties ( see here)
II: LCTVS : Topologies, toplogical vector space, locally convex topologicall spaces and semi-norms, examples
III: Hahn Banach Theorem: Extension, Seperation, strict separation, applications.
IV: Krein-Milman and Caratheordory
Barire Category theorem and open mapping, closed graph, and
uniform boundedness principle, application to Fourier series, closed
VI: Uniform convexity and applications to duality and Radon-Nikodym property, and other approximation tricks.
VII: Spectral Theory for compact operators
Weak toplogies will be disccussed in II and III, and IV. I will
watch out for some applications in quantum information theory.
John Conway: A course in Functional Analysis, second eddition
Graduate Texts in Mathematics 96
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