Generalized averaging operators and matrix summability
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- by Robert E. Atalla
- Proc. Amer. Math. Soc. 38 (1973), 272-278
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313869-X
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Abstract:
A bounded linear operator $T$ on $C(X),X$ compact, is a g.a.o. if it has associated with it a nonnegative projection $S$ satisfying three conditions given below. An ordinary averaging operator is the case $T = S$. We show that if $T$ is g.a.o., then the following problem has a fairly neat solution: What conditions on an operator $R$ are necessary and sufficient for $\operatorname {kernel}(T) \subset \operatorname {kernel}(R)$? Application is made to the problem of the inclusion of one bounded convergence field in another, via the representation of regular matrices as linear operators on $C(\beta N/N)$.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 272-278
- MSC: Primary 47B99; Secondary 40J05, 46J10, 47A35
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313869-X
- MathSciNet review: 0313869