An application of pseudo-inverses. The analytic characteristic of T- regular points for closed operators
The author generalizes his results obtained in Chin. Ann. Math., Ser. A 1, 1988 to the closed operators case. The main result is the following. If T is a closed operator acting in a complex Hilbert space, \(\rho _{sF}(T)\) is the semi-Fredholm domain of T, then \(\lambda \in \rho _{sF}(T)\) is T-regular if and only if there exists a family of holomorphic vector functions \(\{f_ i(\mu)\}_{i\in I}\) defined in some neighborhood \(\Delta\) of \(\lambda\) such that \(\{f_ i(\mu)\}_{i\in I}\) forms a basis of ker(T-\(\mu)\) for \(\mu\) \(\in \Delta\). Thus the author explains why the continuity in the definition of T-regularity implies the analyticity in a sense. Besides, the author gives some applications of the analytic characteristic which improve the results obtained by \textit{C. Apostol} in Rev. Roum. Math. Pures Appl. 21, 155-175 (1976; Zbl 0336.47012).
scientific article; zbMATH DE number 4044502