Topological equivalence in the space of integrable vector-valued functions
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- by Semion Gutman PDF
- Proc. Amer. Math. Soc. 93 (1985), 40-42 Request permission
Abstract:
The Banach space ${L^1}(0,T;X)$ is retopologized by $|||f||| = \max ||\int _a^bfdt||$, $0 \leqslant a \leqslant b \leqslant T$, where $||.||$ is the norm in the given Banach space $X$. It is shown here that this topology coincides with the usual weak topology of ${L^1}(0,T;X)$ on a wide class of weakly compact subsets.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 40-42
- MSC: Primary 46E40; Secondary 28B05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766523-2
- MathSciNet review: 766523