Functional Analysis- II (Compulsory Paper)
Adjoint of an operator on a Hilbert space. Self-adjoint, Positive, Normal and Unitary operators and their properties.Projection on a Hilbert space.
Invariance. Reducibility. Orthogonal projections. Derivatives of a continuous map from an open subset of Banach space to a Banach space.
Rules of derivation. Derivative of a composite, Directional derivative. Mean value theorem and its applications. Partial derivatives and Jacobian Matrix.
Continuously differentiable maps. Higher derivatives. Taylor’s formula. Inverse function theorem. Implicit function theorem. Step function, Regulated function,
Primitives and integrals. Differentiation under the integral sign. Riemann integral of function of real variable with values in normed linear space.
1. G.F.Simmons: Topology and Modern Analysis, McGraw Hill (1963)
2. G.Bachman and Narici : Functional Analysis, Academic Press 1964
3. A.E.Taylor : Introduction to Functional analysis, John Wiley and sons (1958)
1. A.L.Brown and Page : Elements of Functional Analysis, Van-Nastrand Reinehold Com
2.B.V. Limaye: Functional Analysis, New age international.
3.Erwin Kreyszig, Introductory functional analysis with application, Willey.
