Adjoint of an operator on a Hilbert space. Self-adjoint, Positive, Normal and Unitary operators and their properties.Projection on a Hilbert space.
Unit II:
II
15.00
Invariance. Reducibility. Orthogonal projections. Derivatives of a continuous map from an open subset of Banach space to a Banach space.
Unit III:
III
15.00
Rules of derivation. Derivative of a composite, Directional derivative. Mean value theorem and its applications. Partial derivatives and Jacobian Matrix.
Unit IV:
IV
15.00
Continuously differentiable maps. Higher derivatives. Taylor’s formula. Inverse function theorem. Implicit function theorem. Step function, Regulated function,
Unit V:
V
15.00
Primitives and integrals. Differentiation under the integral sign. Riemann integral of function of real variable with values in normed linear space.
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
