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Proceedings of the American Mathematical Society

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$ L\sb{0}$ is $ \omega $-transitive


Authors: N. T. Peck and T. Starbird
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
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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 [Enhancements On Off] (What's this?)

  • [1] N. J. Kalton and N. T. Peck, Quotients of 𝐿_{𝑝}(0,1) for 0≤𝑝<1, Studia Math. 64 (1979), no. 1, 65–75. MR 524022
  • [2] 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 0336313

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630040-7
Keywords: Space of measurable functions, subspace isomorphic to $ \omega $, transitivity of operators, lifting of linear operator, functions with disjoint supports
Article copyright: © Copyright 1981 American Mathematical Society

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