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?References
- M. S. Macphail and A. Wilansky, Linear functionals and summability invariants, Canad. Math. Bull. 17 (1974), 233–242. MR 361528, DOI 10.4153/CMB-1974-046-2
- Albert Wilansky, The $\mu$ 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
- Karl Zeller, Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463–487 (German). MR 39824, DOI 10.1007/BF01175646
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