FUNCTIONAL ANALYSIS-I (Compulsory Paper)
Paper Code:
MAT321
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
15.00
Normed linear spaces, Quotient space of normed linear spaces and its completeness, Banach spaces and examples, Bounded linear transformations.
15.00
Normed linear space of bounded linear transformations, Equivalent norms, Basic properties of finite dimensional normed linear spaces and compactness, Riesz Lemma.
15.00
Open mapping theorem, Closed graph theorem, Uniform boundness theorem, Continuous linear functionals, Hahn-Banach theorem and its consequences.
15.00
Hilbert space and its properties, Orthogonality and Functionals in Hilbert Spaces, Phythagorean theorem, Projection theorem, Orthonormal sets.
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.
- Dileep S. Chauhan, Functional Analysis and calculus in Banach space, JPH.
References:
- B.V. Limaye: Functional Analysis, New age international,III Edition, 2017.
- Erwin Kreyszig, Introductory functional analysis with application, Willey, 2007.
- A.E.Taylor : Introduction to Functional analysis, John Wiley and sons (1958) .
- Graham Allan, H. Garth Dales: Introduction to Banach Spaces and Algebras, Oxford University Press(2010).
- Reinhold Meise, Dietmar Vogt, M. S. Ramanujan : Introduction to Functional analysis, Oxford University Press, 1997.
Academic Year:
