AN APPLICATION OF PSEUDO-INVERSES

THE ANALYTIC CHARACTERISTIC OF T-REGULAR POINTS FOR CLOSED OPERATORS

Abstract

In this paper we shall prove that λ \in {ρ _SF}(T) is T-regular if and only if there exists a family of holomorphic vector functions {{ {f_i}(μ )} _{iε I}} defined in some neighborhood Δ of λ such that {{ {f_i}(μ )} _{iε I}} forms a basis of \ker (T - μ ) for μ \in Δ, where T is a densely defined closed operator acting in a complex Hilbert space, {ρ _SF}(T) is the semi-Fredholm domain of T.