Time and Location:

• The lectures take place on Tuesdays and Thusrsdays from 2pm to 3:15pm in 25-101.

• The first lecture will be on March 8, 2016.

Contact Information:

• Office: 27-314.

• E-mail: ponge [dot] snu [at] gmail [dot] com.

Evaluation:

• Evaluation will be based on homework. There will be about 5-6 homework assignments throughout the semester.

Course Outline:

• Part 1: Banach Spaces and Locally Convex Spaces.

  1. Review of Banach spaces and Hilbert spaces.

  2. The Hahn-Banach theorems.

  3. Applications of Baire category theorem: uniform boundedness principle, open mapping theorem, closed graph theorem.

  4. Locally convex spaces.

  5. Weak topologies. Banach-Alaoglu theorem.

• Part 2: Spectral Theory.

  1. Spectral theory and Banach algebra.

  2. Operators on Hilbert space.

  3. Compact operators and Fredholm theory.

  4. Unbounded operators on Hilbert space.

References for Part 1:

• Main References:

  1. Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, Springer, 2011 (link).

  2. Conway, J.: A Course in Functional Analysis. Graduate Texts in Mathematics, Springer, 2nd Edition, 1994 (link).

• Supplementary Reference:

  • Reed, M.; Simon, B.: Functional Analysis (Methods of Modern Mathematical Physics, Vol. 1). Academic Press, 2nd Edition, 1980.

References for Part 2:

• Main References:

  1. Arveson, W.: A Short Course on Spectral Theory. Graduate Texts in Mathematics, Springer, 2002 (link)

  2. Reed, M.; Simon, B.: Functional Analysis (Methods of Modern Mathematical Physics, Vol. 1). Academic Press, 1980.

• Supplementary Reference:

  • Conway, J.: A Course in Functional Analysis. Graduate Texts in Mathematics, Springer, 2nd Edition, 1994 (link).