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Multipliers on some sequence spaces

Published online by Cambridge University Press:  24 October 2008

J. C. Kurtz
J. C. Kurtz
Affiliation:
Michigan State University
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Abstract

Let ω be the space of all (complex) sequences. If E, F are subspaces of ω and if A is any (infinite) normal matrix, we set

and

If A is the matrix of a sequence–sequence summability transform, Ā and  shall denote the series–sequence and series–series forms of the transform, respectively. The multiplier spaces M(c(Ā), c(Ā)), M(lp(Â), l1(Â)) and M(lp(Â), c(Ā)) are characterized (1 ≤ p < ∞). Partial results are given for the spaces M(c(Ā), lp(Â)) and M(lp(Â), lp(Â)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 393 - 401
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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