Permanence properties of normal structure
Thomas Landes · Pacific Journal of Mathematics · 1984
A new characterization of normal structure is given, which allows to prove permanence properties of normal structure such as preservation under finite direct-sum-operations -e.g., the /^-direct sums, 1 </?< oo -as well as under certain infinite direct-sum-operations -e.g., the /^-direct sums, 1 <p < oo.Furthermore, it is shown that a normed space has isonormal structure -i.e., it is isomorphic to a normally structured space -if and only if it can be mapped by a continuous linear one-to-one operator into some normally structured space.Finally, some problems are discussed, such as preservation of normal structure under the /f-direct-sum-operation.To solve the latter at least partially, a sum-property is introduced which implies normal structure.This sum-property is implied by all known sufficient conditions for normal structure, and it is preserved under all finite direct-sum-operations.