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Some New Product Theorems in Summability

Published online by Cambridge University Press:  20 November 2018

Mangalam R. Parameswaran
Mangalam R. Parameswaran*
Affiliation:
Dept. of Mathematics, University of ManitobaWinnipeg, Manitoba, R3T 2N2, Canada.
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Abstract

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Let A, B denote sequence-to-sequence matrix methods of summability and A · B the “dot” or iteration product defined by (A · B)x = A(Bx) for all sequences x for which this exists. Some inclusion relations are given involving the methods A, B, A · B, B · A and the method defined by the matrix product AB. We take A, B to be of certain types whose products have not been studied extensively before, e.g. H* · Ck or Ck · H* where H* is quasi-Hausdorff (and hence upper triangular) and Ck is a Cesàro matrix (which is lower triangular). The investigations show also a link between the “Product Property” A ⊂ A · B and the translativity properties of A and B.

Keywords

40C0540D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 2 , 01 June 1988 , pp. 182 - 186
Copyright
Copyright © Canadian Mathematical Society 1988

References

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