Approximation of strictly singular and strictly cosingular operators using nonstandard analysis

Brace, J. W.; Kneece, R. Royce

doi:10.1090/S0002-9947-1972-0636378-0

Approximation of strictly singular and strictly cosingular operators using nonstandard analysis
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by J. W. Brace and R. Royce Kneece

Trans. Amer. Math. Soc. 168 (1972), 483-496

DOI: https://doi.org/10.1090/S0002-9947-1972-0636378-0

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Abstract:

The strictly singular operators and the strictly cosingular operators are characterized by the manner in which they can be approximated by continuous linear operators of finite-dimensional range. We make use of linear convergence structures to obtain each class as limit points of the operators with finite-dimensional range. The construction of a nonstandard model makes it possible to replace convergence structures by topologies. Our nonstandard models are called nonstandard locally convex spaces.

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