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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Approximation of strictly singular and strictly cosingular operators using nonstandard analysis
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by J. W. Brace and R. Royce Kneece PDF
Trans. Amer. Math. Soc. 168 (1972), 483-496 Request permission

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.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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