Subadditive functions and a relaxation of the homogeneity condition of seminorms

Author:
Janusz Matkowski

Journal:
Proc. Amer. Math. Soc. **117** (1993), 991-1001

MSC:
Primary 26A12; Secondary 39B72, 46B99

DOI:
https://doi.org/10.1090/S0002-9939-1993-1113646-9

MathSciNet review:
1113646

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every locally bounded above at a point subadditive function such that , for some has to be linear. Using this we show among others that the homogeneity condition of a seminorm in a real linear space can be essentially relaxed to the following condition: there exists an such that for all . A new characterization of the -norm and one-line proofs of Minkowski's and Höder's inequalities are also given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1113646-9

Keywords:
Subadditive functions,
seminorm,
measure space,
characterization of -norm,
Minkowski's inequality,
Hölder's inequality

Article copyright:
© Copyright 1993
American Mathematical Society