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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Summability in amenable semigroups

Author: Peter F. Mah
Journal: Trans. Amer. Math. Soc. 156 (1971), 391-403
MSC: Primary 40.50
MathSciNet review: 0275013
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Abstract: A theory of summability is developed in amenable semigroups. We give necessary and (or) sufficient conditions for matrices to be almost regular, almost Schur, strongly regular, and almost strongly regular. In particular, when the amenable semigroup is the additive positive integers, our theorems yield those results of J. P. King, P. Schaefer and G. G. Lorentz for some of the matrices mentioned above.

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PII: S 0002-9947(1971)0275013-X
Keywords: Amenable semigroups, extremely amenable semigroups, almost convergent, almost convergent functions, invariant mean, almost regular matrices, almost Schur matrices, strongly regular matrices, almost strongly regular matrices
Article copyright: © Copyright 1971 American Mathematical Society