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Proceedings of the American Mathematical Society
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?


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0447876-7
PII: S 0002-9939(1977)0447876-7
Keywords: Summability, nonreplaceable matrix, test function, matrix representation
Article copyright: © Copyright 1977 American Mathematical Society