The spaces of functions of finite upper -variation

Author:
Robert R. Nelson

Journal:
Trans. Amer. Math. Soc. **253** (1979), 171-190

MSC:
Primary 46E30; Secondary 28B05

DOI:
https://doi.org/10.1090/S0002-9947-1979-0536941-8

MathSciNet review:
536941

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *y* be a Banach space, , and be the semi-normed space of *Y*-valued Bochner measurable functions of a real variable which have finite upper *p*-variation. Let be the space of -equivalence classes. An averaging operator is defined with the aid of the theory of helixes in Banach spaces, which enables us to show that the spaces are Banach spaces, to characterize their members, and to show that they are isometrically isomorphic to Banach spaces of *Y*-valued measures with bounded *p*-variation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0536941-8

Keywords:
Upper *p*-variation,
average vector,
helixes in Banach spaces,
translation operators,
Lebesgue-Bochner integral,
chordal length function,
absolutely continuous function,
bounded variation

Article copyright:
© Copyright 1979
American Mathematical Society