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Approximation of Strictly Singular and Strictly Cosingular Operators Using Nonstandard Analysis

J. W. Brace and R. Royce Kneece
Transactions of the American Mathematical Society
Vol. 168 (Jun., 1972), pp. 483-496
DOI: 10.2307/1996187
Stable URL: http://www.jstor.org/stable/1996187
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Approximation of Strictly Singular and Strictly Cosingular Operators Using Nonstandard Analysis
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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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