Abstract
In this note a theorem of B. Gramsch [6] on one-sided meromorphic inverses of Semi-Fredholmoperator valued holomorphic functions is generalized to holomorphic functions on a Stein space with values in the set of Semi-Fredholm-operators between two Banach spaces. By the way, a theorem of G.R. Allan [1] on holomorphic one-sided inverses is generalized to holomorphic functions on a Stein space with values in certain paraalgebras (c.f. [5]). As an application of that a duality theorem for holomorphic bases of finite dimensional subspaces of (F)- and (DF)-spaces is proved (c.f. [3]).
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Kaballo, W. Über holomorphe und meromorphe einseitige Inverse. Manuscripta Math 13, 1–13 (1974). https://doi.org/10.1007/BF01168738
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DOI: https://doi.org/10.1007/BF01168738