A 𝑣-integral representation for the continuous linear operators on spaces of continuously differentiable vector-valued functions

Edwards, J. R.; Wayment, S. G.

doi:10.1090/S0002-9939-1971-0281031-3

A $v$-integral representation for the continuous linear operators on spaces of continuously differentiable vector-valued functions
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by J. R. Edwards and S. G. Wayment PDF

Proc. Amer. Math. Soc. 30 (1971), 263-270 Request permission

Abstract:

Suppose X and Y are linear normed spaces, and ${C_1}$ is the space of continuously differentiable functions from [0, 1] into X. The authors give a represention theorem for the linear operators from ${C_1}$ into Y in terms of the v-integral operating on the function as opposed to the derivative of the function.

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