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$L_0$ is $\omega$-Transitive
N. T. Peck and T. Starbird
Proceedings of the American Mathematical Society
Vol. 83, No. 4 (Dec., 1981), pp. 700-704
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044237
Page Count: 5
You can always find the topics here!Topics: Isomorphism, Mathematical theorems, Topological theorems, Mathematical functions, Linear transformations, Mathematical sets, Mathematical sequences, Homeomorphism, Integers
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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.
Proceedings of the American Mathematical Society © 1981 American Mathematical Society