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Contraction Property of the Operator of Integration
Published online by Cambridge University Press: 20 November 2018
Abstract
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(—∞, ∞).
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- Copyright © Canadian Mathematical Society 1975
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