Banach Spaces, Hilbert Spaces
Bounded linear operators, Duality, Representation theorems for linear functionals
Uniform boundedness principle, Open mapping and Closed graph theorem
Weak Convergence, Weak and Weak* Topologies
Compact operators
Hahn-Banach’s Theorems, Locally convex spaces
Spectral theory
Banach Algebras, Gelfand representation theorem
Fredholm theory
Unbounded operators
P. D. Lax, Functional analysis, Pure and Applied Mathematics, Wiley.
M. C. Reed and B. Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press.
J. B. Conway, A course in functional analysis, Graduate Texts in Mathematics, 96, Springer.
H. R. Brezis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer.
E. M. Stein and R. Shakarchi, Functional analysis, Princeton Lectures in Analysis, Princeton Univ. Press.
G. Teschl, Topics in Linear and Nonlinear Functional Analysis, Graduate Studies in Mathematics, AMS.
K. Yosida, Functional analysis, Classics in Mathematics, Springer.
R. J. Zimmer, Essential results of functional analysis, Chicago Lectures in Mathematics, Univ. Chicago Press.
Real Analysis, Linear Algebra, Basic Complex Analysis, Basic Topology, Basic Measure Theory (especially Lp spaces), Familiarity with Fourier series, ODEs and PDEs will be helpful.
Assignments×20% + Presentation/Oral exam×30% + Final Exam×50%
To pass(DD), one needs to score at least 40% in the course.
The Final exam will cover the entire course.