Über tonnelierte raume.
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.
We construct the example of the title.
We give an example in the Hilbert space of two subsets which are absorbing for the class of topologically complete spaces, but for which there exists no homeomorphism of onto itself mapping one of these subsets onto the other.