Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 348: Topics in function theoretic operator Theory

Credits: 3:0

Prerequisite courses: MA 219, MA 222, MA 223 and MA 224

Banach algebras – Gelfand theory, L-infinity functional calculus for bounded normal operators, Pick - Nevanlinna and Caratheodory Interpolation problems, Distinguished varieties in the bidisc.

Suggested books and references:

1. Douglas, Ronald G., Banach algebra techniques in operator theory. Second edition, Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998.
2. Conway, John B., A course in functional analysis. Second edition, Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990.
3. Agler, Jim; McCarthy, John Edward; Young, Nicholas, Operator analysis—Hilbert space methods in complex analysis, Cambridge Tracts in Mathematics, 219. Cambridge University Press, Cambridge, 2020.
4. Bhattacharyya, Tirthankar; Kumar, Poornendu; Sau, Haripada, Distinguished varieties through the Berger-Coburn-Lebow theorem., Anal. PDE 15 (2022), no. 2, 477–506.

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