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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Approximation of strictly singular and strictly cosingular operators using nonstandard analysis


Authors: J. W. Brace and R. Royce Kneece
Journal: Trans. Amer. Math. Soc. 168 (1972), 483-496
MSC: Primary 47D15; Secondary 02H25, 47B05
DOI: https://doi.org/10.1090/S0002-9947-1972-0636378-0
MathSciNet review: 0636378
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0636378-0
Keywords: Approximation of linear operators, strictly singular operators, strictly cosingular operators, nonstandard analysis, convergence structure, nuclear operators, compact operator
Article copyright: © Copyright 1972 American Mathematical Society