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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some invariant properties on summability domains
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by Shen Yue Kuan PDF
Proc. Amer. Math. Soc. 64 (1977), 248-250 Request permission

Abstract:

Let A be an infinite matrix. Each $f \in {c’_A}$ has a representation $f(x) = \alpha {\lim _A}x + t(Ax) + rx$. The purpose of this short article is to answer the following problems raised by Wilansky. 1. Does $\alpha$ invariantly unique imply ${\alpha ^ \bot }$ invariant? 2. Does A not-replaceable imply ${\alpha ^ \bot }$ invariant? 3. Could a function $f \in {c’_A}$ with $\alpha$ uniquely zero have a matrix representation? 4. Is the set of test functions invariant?
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 248-250
  • MSC: Primary 40H05
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0447876-7
  • MathSciNet review: 0447876