MA 844 Topics in Analysis II (Aut 2011)

Lectures: Mon 9:30 to 10:25 am, Tue 10:35 to 11:30 am, Thu 11.35 am to 12:30 pm in Room 114

Informations about the course:

Content:

Basic theory of C*-algebras and von Neumann algebras: positive elements, Gelfand theory, continuous functional calculus, weak topologies, Predual, double commutant theorem, Kaplansky density theorem, ideals, GNS construction, representation theorem of W*-algebras, second dual of C*-algebras, Factors.

Text/References:

1. W. Arveson: An Invitation to C*-algebras, Springer

2. J. B. Conway: A course in Operator Theory, American Mathematical Society

3. K. Davidson: C*-algebras by Examples, American Mathematical Society

4. R. V. Kadison, J. R. Ringrose: Fundamental of Theory of Operator Algebras-I and II, Academic Press.

5. S. Sakai: C*-algebras and W*-algebras, Springer

6. M. Takesaki: Theory of Operator Algebras, Springer

Topics of student's talks (Fri 2-3:30 pm in Room 114):

1. Spectrum is nonempty closed and bounded- G. Gorai ([8])

2. Banach-Alaoglu theorem- G. Nair ([8])

3. Dilation theory- S. Goyal, M.M. Radhika ([10],[11],[12],[14])

4. Inner functions and Beurling's theorem- Anbu ([2],[12],[14])

5. Canonial commutation relations (CCR)- G. Mallick ([7])

6. Uniqueness of CCR- Sajith ([7],[15])

7. Cuntz algebras- P. Bag ([3],[9])

8. Factors- S. Poddar, H. Trivedi ([2],[4],[5],[6],[13])

Additional references for talks: pdf

As assignments students can take up some of the exercises given in books listed under references.