An application of pseudo-inverses - the analytic characteristic of T-regular points for closed operators
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概要
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In this paper we shall prove that λ \in {ρ <SUB>SF</SUB>}(T) is T-regular if and only if there exists a family of holomorphic vector functions {{ {f_i}(μ )} <SUB>iε I</SUB>} defined in some neighborhood Δ of λ such that {{ {f_i}(μ )} <SUB>iε I</SUB>} 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 <SUB>SF</SUB>}(T) is the semi-Fredholm domain of T.
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