Real Analysis II

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Typical Scheduling: 
Every spring semester

This course is a continuation of MATH 6337. It covers L^p and Hilbert spaces, and an introduction to operator theory and functional analysis.


This course is equivalent to MATH 6580. Students should not be able to obtain credit for both MATH 6580 and MATH 6338.


Math 6337 or consent of the school

Course Text: 

At the level of Conway, “A Course in Functional Analysis,” 2nd edition, or Heil lecture notes, “Operator Theory and Functional Analysis”.

Topic Outline: 
  • Banach spaces, L^p spaces, completeness, Hölder's, Minkowski’s, Jensen’s inequalities, Hilbert spaces.
  • Baire Category Theorem.
  • Bounded operators on Banach and Hilbert spaces.
  • Riesz Representation Theorem and adjoints of operators on Hilbert spaces.
  • Hahn–Banach Theorem and its applications, including dual of L p and adjoints of operators on Banach spaces.
  • Uniform Boundedness, Open Mapping, and Closed Graph Theorems.
  • Additional topics at instructor’s discretion as time permits.