OPERATOR THEORY

Theory of bounded linear operators. Basic theorems of functional analysis. Bounded operators in Hilbert spaces. Weak and strong convergence, uniform convergence. Positive operators. Functionals. Properties of bounded linear operators. The notion and the significance of the spectrum. Physical interpretation of the spectrum. The spectrum of normal and self-adjoint operators. Various types of bounded operators (isometric, unitary, projective, compact, etc). The spectrum of self-adjoint and compact operators. Theory of unbounded linear operators. Closed operators, hermitian, symmetric, self-adjoint (unbounded) operators.