The Associative Part of a Convergence Domain is Invariant
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 147-148

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Of special interest in summability theory are those conservative matrices possessing the "mean-value property". If c A ={x: Ax ∊ c} denotes the convergence domain of a conservative matrix A, then A has the mean-value property in case, for each x in c A , there exists M = M(A, x) > 0 such that 1 This property has been considered by many writers and has been shown, among other things, to be equivalent to the requirement that the matrix be associative, i.e., for each x in c A 2
Sember, John J. The Associative Part of a Convergence Domain is Invariant. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 147-148. doi: 10.4153/CMB-1970-033-2
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[1] 1. Wilansky, A., Distinguished subsets and summability invariants, J. Analys. Math. 12 (1964), 327-350. Google Scholar

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