Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T23:26:52.155Z Has data issue: false hasContentIssue false
  • English
  • Français

On the relationship between a summability matrix and its transpose

Part of: General summability methods Functional analytic methods in summability Direct theorems on summability

Published online by Cambridge University Press:  09 April 2009

J. Swetits
J. Swetits
Affiliation:
Department of Mathematical and Computing Sciences Old Dominion UniversityNorfold, Virginia 23508, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let E, F be sequence spaces and A an infinite matrix that maps E to F. Sufficient conditions are given so that the transposed matrix maps Fβ to Eβ.

MSC classification

Secondary: 40C05: Matrix methods 40D25: Inclusion and equivalence theorems 40H05: Functional analytic methods in summability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 362 - 368
Copyright
Copyright © Australian Mathematical Society 1979

References

Bennett, G. (1974), ‘A new class of sequence spaces with applications in summability theory’, J. Reine Angew. Math. 266, 49–75.Google Scholar
Dawson, D. F. (1976), ‘Matrix maps of null sequences’, Notices Amer. Math. Soc. 23, A-134, Abstract No. 731–40–2.Google Scholar
Garling, D. J. H. (1967a), ‘The β and γ duality of sequence spaces’, Proc. Camb. Phil. Soc. 63, 963–981.Google Scholar
Garling, D. J. H. (1967b), ‘On topological sequence spaces’, Math. Proc. Cambridge Philos. Soc. 63, 997–1019.Google Scholar
Jakimovski, A. and Livne, A. (1971), ‘General Kojima-Topelitz like theorems and consistency theorems’, J. Analyse Math. 24, 323–368.Google Scholar
Jakimovski, A. and Livne, A. (1972), ‘On matrix transformations between sequence spaces’, J. Analyse Math. 25, 345–370.CrossRefGoogle Scholar
Jakimovski, A. and Russell, D. C. (1972), ‘Matrix mappings between BK spaces’, Bull. London Math. Soc. 4, 345–353.Google Scholar
Mcphail, M. S. (1951), ‘Some theorems on absolute summability’, Canad. J. Math. 3, 386–390.CrossRefGoogle Scholar
Sargent, W. L. C. (1964), ‘On sectionally bounded SAT spaces’, Math. Zei. 83, 57–66.Google Scholar
Skerry, H. B. (1974), ‘On matrix maps of entire sequences’, Pacific J. Math. 51, 563–570.Google Scholar
Swetits, J. (1978), ‘A characterization of a class of barrelled sequence spaces’, Glasgow Math. J. 19, 27–31.Google Scholar
Vermes, P. (1957), ‘The transpose of a summability matrix’, Coll. Théorie des Suites (Bruxelles), 60–86.Google Scholar
Zeller, K. (1951), ‘Abschnittskonvergenz in FX-Räumen’, Math. Zeit. 55, 55–70.CrossRefGoogle Scholar