%0 Journal Article
%T Amaximal extension of Kothe\'s homomorphism theorem
%J -
%D 1992
%R DOI Code: 10.1285/i15900932v12p229
%X 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. K£¿the 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, K£¿the'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 K£¿the and allows us to replace £¿< \aleph_0£¿ with £¿< c £¿. This is, easily, the best possible extension as regards codimension of
%U http://siba-ese.unisalento.it/index.php/notemat/article/view/1378