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

Authors: J. R. Edwards and S. G. Wayment
Journal: Proc. Amer. Math. Soc. 30 (1971), 263-270
MSC: Primary 47.25; Secondary 28.00
MathSciNet review: 0281031
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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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Keywords: Generalized Stieltjes-type integral, convex with respect to length, 1-Gowurin, differentiable vector-valued functions, weak sequential extension
Article copyright: © Copyright 1971 American Mathematical Society

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