A -integral representation for linear operators on a space of continuous vector-valued functions

Authors:
J. R. Edwards and S. G. Wayment

Journal:
Proc. Amer. Math. Soc. **30** (1971), 260-262

MSC:
Primary 47.25; Secondary 28.00

MathSciNet review:
0281030

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note an analytic representation is given for continuous linear operators from into a linear normed space *Y* where is the space of continuous functions on [0, 1] with values in a linear normed space *X*.

**[1]**J. R. Edwards and S. G. Wayment,*Representations for transformations continuous in the 𝐵𝑉 norm*, Trans. Amer. Math. Soc.**154**(1971), 251–265. MR**0274704**, 10.1090/S0002-9947-1971-0274704-4**[2]**Don H. Tucker,*A note on the Riesz representation theorem*, Proc. Amer. Math. Soc.**14**(1963), 354–358. MR**0145334**, 10.1090/S0002-9939-1963-0145334-0**[3]**Don H. Tucker,*A representation theorem for a continuous linear transformation on a space of continuous functions*, Proc. Amer. Math. Soc.**16**(1965), 946–953. MR**0199722**, 10.1090/S0002-9939-1965-0199722-9

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DOI:
https://doi.org/10.1090/S0002-9939-1971-0281030-1

Keywords:
Continuous linear operator,
vector-valued function,
representation theorem,
convex-Gowurin,
*v*-integral,
polygonal function

Article copyright:
© Copyright 1971
American Mathematical Society