On the normability of the intersection of $L_{p}$ spaces
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- by Wayne C. Bell PDF
- Proc. Amer. Math. Soc. 66 (1977), 299-304 Request permission
Abstract:
The set ${L_\omega } = \bigcap \nolimits _{p = 1}^\infty {{L_p}[0,1]}$ is not equal to ${L_\infty }[0,1]$ since ${L_\omega }$ contains the function $- \ln x$. Using the theory of ${L_p}$ spaces for finitely additive set functions developed by Leader [9] we will prove several necessary and sufficient conditions for the normability of a generalization of ${L_\omega }$. These include the equality and finite dimensionality of all the ${L_p}$ spaces, $p \geqslant 1$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 299-304
- MSC: Primary 46E99; Secondary 28A10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0482154-1
- MathSciNet review: 0482154