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- W2100626524 abstract "If A = ( a m, n ) is a regular matrix, then for any sequence x = { x n }, A m ( x ) will denote the transform and A -lim x denotes if that limit exists. We shall denote by the set of bounded sequences which are summed by A . If B is another regular matrix with then we say that B is b -stronger than A . In that case B must be b-consistent with A (see (4) and (6)), i.e. if then If { μ n } is a sequence of positive real numbers with we say that A and B are ( μ n )-consistent if every sequencer x = { x n } satisfying x n = 0( μ n ) which is summed by both A and B is summed to the same value by both matrices. A finite set of matrices A 1 , A 2 , …, A N is said to be simultaneously ( μ n )-inconsistent ( b-consistent ) if whenever is summed by A i with ( i = l, 2, …, N ) then implies that The set of sequences, is denoted by" @default.
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- W2100626524 date "1967-01-01" @default.
- W2100626524 modified "2023-10-16" @default.
- W2100626524 title "Summability fields which span the bounded sequences" @default.
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- W2100626524 doi "https://doi.org/10.1017/s0305004100040937" @default.
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