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Contraction Property of the Operator of Integration

Published online by Cambridge University Press:  20 November 2018

Ludvik Janos
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Abstract

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It is shown that the operator of integration Fy(x) = ∫x0y(t) dt defined on the space C(—∞, ∞) of all continuous real valued functions on (—∞, ∞) is a contraction relative to a certain family of seminorms generating the topology of uniform convergence on compacta. However, as a contrast to this it is proved that F is not contractive with respect to any metric on C(—∞, ∞) inducing the above topology on C(—∞, ∞).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 367 - 369
Copyright
Copyright © Canadian Mathematical Society 1975

References

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