Über Endomorphismen mit dichten Bahnen.
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.
The uniformly Kadec-Klee property in Köthe-Bochner sequence spaces , where is a Köthe sequence space and is an arbitrary separable Banach space, is studied. Namely, the question of whether or not this geometric property lifts from and to is examined. It is settled affirmatively in contrast to the case when is a Köthe function space. As a corollary we get criteria for to be nearly uniformly convex.
We prove that the quasi-Banach spaces and (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.