Functional Analysis- I
Paper Code:
MAT 321
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
Unit I:
I
15.00
Normed linear spaces. Quotient space of normed linear spaces and its completeness. Banach spaces and examples. Bounded and continuous linear transformations.
Unit II:
II
15.00
Normed linear space of bounded linear transformations. Equivalent norms. Basic properties of finite dimensional normed linear spaces and compactness. Reisz Lemma.
Unit III:
III
15.00
Multilinear mapping. Open mapping theorem. Closed graph theorem. Uniform boundness theorem. Continuous linear functionals. Hahn-Banach theorem and its consequences.
Unit IV:
IV
15.00
Dual spaces with examples. Inner product spaces. Hilbert space and its properties. Orthogonality and Functionals in Hilbert Spaces. Phythagorean theorem, Projection theorem, Orthonormal sets.
Unit V:
V
15.00
Bessel’s inequality, Complete orthonormal sets, Parseval’s identity, Structure of a Hilbert space, Riesz representation theorem.
Essential Readings:
- G.F.Simmons: Topology and Modern Analysis, McGraw Hill (1963)
- G.Bachman and Narici : Functional Analysis, Academic Press 1964
- A.E.Taylor : Introduction to Functional analysis, John Wiley and sons (1958)
- A.L.Brown and Page : Elements of Functional Analysis, Van-Nastrand Reinehold Com
- B.V. Limaye: Functional Analysis, New age international.
- Erwin Kreyszig, Introductory functional analysis with application, Willey.
- Dileep S. Chauhan, Functional Analysis and calculus in Banach space, JPH.
Academic Year:
