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Proceedings of the American Mathematical Society

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Some invariant properties on summability domains

Author: Shen Yue Kuan
Journal: Proc. Amer. Math. Soc. 64 (1977), 248-250
MSC: Primary 40H05
MathSciNet review: 0447876
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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?

References [Enhancements On Off] (What's this?)

  • [1] M. S. Macphail and A. Wilansky, Linear functional and summability invariants, Canad. Math. Bull. 17 (1974), 233-242. MR 50 #13973. MR 0361528 (50:13973)
  • [2] A. Wilansky, On the $ \mu $ property of FK spaces, Comment. Math., Special Volume dedicated to W. Orlicz on the occasion of his 75th birthday, 1978 (to appear). MR 504180 (81k:40009)
  • [3] K. Zeller, Allegemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463-487. MR 12, 604. MR 0039824 (12:604e)

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Keywords: Summability, nonreplaceable matrix, test function, matrix representation
Article copyright: © Copyright 1977 American Mathematical Society

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