Geodesic
Contraction Property of the Operator of Integration
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 367-369

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It is shown that the operator of integration Fy(x) = ∫x 0y(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(—∞, ∞). 
Contraction Property of the Operator of Integration. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 367-369. doi: 10.4153/CMB-1975-066-0
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