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On a summability theorem of Berg, Crawford and Whitley

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling  and
A. Wilansky
D. J. H. Garling
Affiliation:
St John's College, Cambridge and Lehigh University, Bethlehem, Pennsylvania
A. Wilansky
Affiliation:
St John's College, Cambridge and Lehigh University, Bethlehem, Pennsylvania
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Extract

We recall that a matrix A is said to sum a sequence x if Axε c, the space of all convergent sequences, and that A is conservative if it sums every convergent sequence. If A is conservative, A defines a continuous linear operator on c. Berg (2), Crawford (3)and Whitley (9) have proved the following theorem:

Theorem 1. A conservative matrix sums no bounded divergent sequence if and only if,considered as an operator on c, it is range closed and has finite-dimensional null-spac

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 495 - 497
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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