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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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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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