$L_{0}$ is $\omega$-transitive
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- by N. T. Peck and T. Starbird PDF
- Proc. Amer. Math. Soc. 83 (1981), 700-704 Request permission
Abstract:
Let ${L_0}$ be the space of measurable functions on the unit interval. Let $F$ and $G$ be two subspaces of ${L_0}$, each isomorphic to the space of all sequences. It is proved that there is a linear homeomorphism of ${L_0}$ onto itself which takes $F$ onto $G$. A corollary of this is a lifting theorem for operators into ${L_0}/F$, where $F$ is a subspace of ${L_0}$ isomorphic to the space of all sequences.References
- N. J. Kalton and N. T. Peck, Quotients of $L_{p}(0,\,1)$ for $0\leq p<1$, Studia Math. 64 (1979), no. 1, 65–75. MR 524022
- S. Kwapień, On the form of a linear operator in the space of all measurable functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 951–954 (English, with Russian summary). MR 336313
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 700-704
- MSC: Primary 46E30; Secondary 46B25, 46G15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630040-7
- MathSciNet review: 630040