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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
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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
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