Theory of linear operators in Hilbert space

linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the rules of quantum mechanics in the one-body case. in particular, we introduce and discuss the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators, self-adjointness criterion and stability of self-adjointness under small perturbations, spectrum, isometric and unitary operators, spectral