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Core-Consistency and Total Inclusion for Methods of Summability

Published online by Cambridge University Press:  20 November 2018

G. G. Lorentz  and
A. Robinson
G. G. Lorentz
Affiliation:
Wayne University
A. Robinson
Affiliation:
University of Toronto
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We shall consider methods of summation A, B, … defined by matrices of real elements (amn), (bmn), (m, n = 1, 2, …) which are regular, that is, have the three well-known properties of Toeplitz (4, p. 43). A method A is said to be core-consistent with the methodBfor bounded sequences if the A-core (3, p. 137; and 4, p. 55) of each real bounded sequence is contained in its B-core. B is totally included in A, B ≪A, if each real sequence which is B-summable to a definite limit (this limit may be finite or infinite of a definite sign) is also A-summable to the same limit.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 27 - 34
Copyright
Copyright © Canadian Mathematical Society 1954

References

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