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A remark on metrically convergent series in F-spaces*

Published online by Cambridge University Press:  24 October 2008

H. M. Charsky
H. M. Charsky
Affiliation:
Israel Institute of Technology
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Extract

Let X be an F-space, not necessarily locally convex, with a quasi-norm ‖x‖ (see (7), p. 31). The series

of elements of X is commutatively convergent if and only if converges for every permutation {Yn}nεω of {Xn}nεω.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 613 - 615
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Bourbaki, N.Elements of mathematics, General topology, Part 1 (Hermann and Addison-Wesley, 1966).Google Scholar
(2)Dunford, N. and Schwartz, J. T.Linear operators, Part 1, General theory (Interscience Publishers, Inc. 1958).Google Scholar
(3)Dvoretzky, A.On series in linear topological spaces. Israel J. Math. 1 (1963), 37–47.CrossRefGoogle Scholar
(4)Dvoretzky, A. and Rogers, C. A.Absolute and unconditional convergence in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 192–197.CrossRefGoogle ScholarPubMed
(5)Rolewicz, S.On a certain class of linear metric spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 5 (1957), 471–473.Google Scholar
(6)Rolewicz, S.On a generalization of the Dvoretzky–Rogers theorem. Colloq. Math. VIII, 1 (1961), 103–106.Google Scholar
(7)Yosida, K.Functional analysis (Springer Verlag, 1965).Google Scholar