Minkowskische und absolute Geometrie I.
Much of this paper will be concerned with the proof of the following
Let , denote the space of Bessel potentials , , with norm . For integer can be identified with the Sobolev space . One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the positive cone...
Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove that every...
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