Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-07T11:13:54.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Markov Projections and Matrix Summability

Published online by Cambridge University Press:  20 November 2018

Robert E. Atalla
Robert E. Atalla*
Affiliation:
Dept. of Mathematics, Ohio University, Athens,Ohio 45701
Rights & Permissions [Opens in a new window]

Extract

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.

In [A1] is defined a class of Markov operators on C(X) (X compact T2), called Generalized Averaging Operators (g.a.o.) which yield an easy solution to the following problem: given a fixed Markov operator T, find necessary and sufficient conditions on any other Markov operator R for the relation ker T ⊂ker R to hold. The main application of this is to inclusion relations between matrix summability methods.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 311 - 316
Copyright
Copyright © Canadian Mathematical Society 1979

References

[A1]. Atalla, R., Generalized averaging operators and matrix summability, Proc. Amer. Math. Soc. 38 (1973), 272-278.Google Scholar
[A2]. Atalla, R., On the inclusion of a bounded convergence field in the space of almost convergent sequences, Glasgow Math. J. 13 (1972), 82-90.Google Scholar
[A3]. Atalla, R., Inclusion theorems for bounded convergence fields, J. Indian Math. Soc. 38 (1974), 405-410.Google Scholar
[A4]. Atalla, R., Generalized almost convergence vs. matrix summability, preprint.Google Scholar
[D]. Day, M., Normed linear spaces. Springer, New York, 1962 (1st éd.).Google Scholar
[L]. Leibowitz, G., Lectures on complex function algebras, Scott-Foresman, Glenview, 111., 1970.Google Scholar
[L1]. Lloyd, S., A mixing condition for left invariant means, Trans. Amer. Math. Soc. 125 (1966), 461-481.Google Scholar
[P]. Petersen, G., Factor sequences and their algebras, Jber. Deutch. Math. Verein. 74 (1973), 182-188.Google Scholar