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- W1548696173 abstract "In 1958, Prof. T.Kato gave the following perturbation theorem: Let , and be subspaces of Banach spaces E and F, respectively, and let be a linear surjective map from onto with closed graph in .If , then f is open and is closed in F [4]. Ten years later, Prof Dr. G. Kothe gave two generalizations [5] which enhanced and were enhanced by considerations of codimension [7], Baire-like (BL) spaces [11a], and quasi-Baire (QB) spaces [11a, 9], and thus, together with a Robertson-Robertson Closed Graph Theorem (cf. [14]), provided significant external impetus for the early study of strong barelledness conditions. Viewed as yet another version of the Kato result, Kothe's Homomorphism Theorem replaces «Banach spaces» with the more general «(LF)-spaces» (cf. 8.4.13 of [6]). Here, again, strong barelledness [12] kindly repays Kothe and allows us to replace « ." @default.
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- W1548696173 date "1992-01-01" @default.
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- W1548696173 title "Amaximal extension of Kothe's homomorphism theorem" @default.
- W1548696173 doi "https://doi.org/10.1285/i15900932v12p229" @default.
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