Über analytische Fortsetzung in Banachräumen.
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.
Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {an*} mean the decreasing rearrangement of a sequence {|an|}. A sequence space lφ,E with symmetric (quasi)norm || {φ(n)an*} ||Ê is called ultrasymmetric, because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λφ and Mφ. We study properties of the spaces lφ,E for all admissible...