Dual space considerations: Representation of duals of the spaces Coo
with p-norms, Co and c with supremum-norm, lp, C [a, b] and Lp.
Reflexivity; Weak and weak* convergences.
Operators on Banach and Hilbert spaces: Compact operators between
normed linear spaces; Integral operators as compact operators; Adjoint of
operators between Hilbert spaces; Self-adjoint, normal and unitary
operators; Numerical range and numerical radius; Hilbert-Schmidt
operators.
Spectral results for Banach and Hilbert space operators: Eigen spectrum,
approximate eigen spectrum; Spectrum and resolvent; Spectral radius
formula; Spectral mapping theorem; Riesz-Schauder theory; Spectral
results for normal, self-adjoint and unitary operators; Functions of self-adjoint
operators.
Spectral representation of operators: Spectral theorem and singular value
representation for compact self-adjoint operators; Spectral theorem for
selfadjoint
operators.
- Teacher: kunal Kunal Krishna Mukherjee