## Steinhaus type theorems for summability matrices

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- by I. J. Maddox PDF
- Proc. Amer. Math. Soc.
**45**(1974), 209-213 Request permission

## Abstract:

Necessary and sufficient conditions are given for an infinite matrix to sum all bounded strongly summable sequences. It is shown that the Borel matrix does not sum all such sequences. A corollary is that the bounded summability field of the Borel method is strictly contained in that of the $(C,1)$ method. Also, it is proved that no coregular matrix can almost sum all bounded sequences—a generalization of Steinhaus’ theorem.## References

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## Additional Information

- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**45**(1974), 209-213 - MSC: Primary 40C05; Secondary 40G10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0364938-0
- MathSciNet review: 0364938