Über vektorwertige meromorphe Funktionen.
We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C*-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C*-algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C*-algebras.
The ultrapowers, relative to a fixed ultrafilter, of all the Köthe function spaces with non trivial concavity over the same measure space can be represented as Köthe function spaces over the same (enlarged) measure space. The existence of a uniform homeomorphism between the unit spheres of two such Köthe function spaces is reproved.