Consequences of the existence of a non-compact operator between nuclear Köthe spaces
Let E and F be nuclear Köthe spaces with continuous norm. Then using the result: ''Every linear continuous map form E into F is compact if and only if every continuous generalized diagonal map (i.e. composition of a permutation by a diagonal map) from E into F is compact'', it is proved that if there exists a non-compact linear continuous map from E into F then E and F have a common step space up to isomorphism in each of the following cases: 1) E is regular and F is isomorphic to a subspace of E. 2) F is regular and E is isomorphic to a quotient space of F. 3) E and F satisfy a certain splitting condition. Consequences in some particular cases are also obtained.
nuclear Köthe spaces with continuous norm
scientific article; zbMATH DE number 3867988