• Instructor : M. Rajesh Kannan
• Instructor's mail id : rajeshkannan@math.iith.ac.in
• Segment : 1-6
• Duration : 28-07-2025 to 17-11-2025 (~43 Lectures)
• Class Schedule: Monday 10am-10.55am; Wednesday 9am-9.55am; Thursday 11am-11.55am. (B-slot).
• Venue: MA - 01 (Maths Building)
• Office hours: By appointment (MA201).
• Exams: Mid 1 - 30-08-2025: Mid 2 - 27-09-2025: End - 20-11-2025.

(Possible) Syllabus :

Review of metric spaces. Normed linear spaces. Non-compactness of the unit ball in infinite dimensional normed linear spaces. Product and quotient spaces. Banach spaces, Hilbert spaces. Linear maps. Boundedness and continuity. Linear isometries, linear functionals. Examples.

Hahn-Banach extension theorem, applications. Banach-Steinhaus theorem, closed graph theorem, open mapping theorem and bounded inverse theorem, Spectrum of a bounded operator.

Gram-Schmidt orthogonalization. Bessel's inequality, Riesz-Fisher theorem. Orthonormal basis, Parseval's identity, Projection, orthogonal decomposition. Bounded linear functionals on Hilbert spaces.