Near-standard compact internal linear operators
Wilhelmus A. J. Luxemburg · 2020
In order to apply A. Robinson’s celebrated result that a subset of a topological space is compact if and only if all its entities in an enlargement are near-standard it is often necessary to obtain an intrinsic characterization of the near-standard entities that are involved. For instance, in the case of Ascoli’s theorem its nonstandard proof is based on the characterization of the near-standard internal continuous functions. The chapter presents a more intrinsic characterization of ns-compactness. For special classes of internal linear operators such as the self-adjoint and normal operators the characterization of being near-standard compact turns out to be similar to Robinson’s characterization of compactness for standard bounded linear operators. Using his characterization of compact sets, Robinson derived at the following characterization of compact linear operators.