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Proceedings of the American Mathematical Society

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

 

 

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 functionals and summability invariants, Canad. Math. Bull. 17 (1974), 233–242. MR 0361528
  • [2] Albert Wilansky, The 𝜇 property of FK spaces, Comment. Math. Special Issue 1 (1978), 371–380. Special issue dedicated to Władysław Orlicz on the occasion of his seventy-fifth birthday. MR 504180
  • [3] Karl Zeller, Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463–487 (German). MR 0039824

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0447876-7
Keywords: Summability, nonreplaceable matrix, test function, matrix representation
Article copyright: © Copyright 1977 American Mathematical Society