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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalized averaging operators and matrix summability


Author: Robert E. Atalla
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
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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)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313869-X
Keywords: Markov operator, averaging operator, projection, $ C(X)$, regular matrix, convergence field, inclusion of convergence fields
Article copyright: © Copyright 1973 American Mathematical Society