MA 843 Topics in Analysis I (Autumn 2019)

Lectures: Mon, Thu- 5:30 to 6:55 pm in Room 105

Informations about the course:

Content:

C*-algebras and cp maps: positive elements, Gelfand theory, continuous functional calculus, weak topologies, Predual, double commutant theorem, Kaplansky density theorem, ideals, GNS construction, Hahn-Hellinger theorem, positive maps, Stinespring theorem, Choi's theorem, Schur product.

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. V. S. Sunder: Functional Analysis- Spectral Theory, TRIM, Hindustan Book Agency.

6. V. Paulsen: Completely Bounded Maps and Operator Algebras, Cambridge Univ. Press.