A rigid subspace of 𝐿₀

Author:

Kalton N. J.,Roberts James W.

Abstract

We construct a closed infinite-dimensional subspace of L 0 ( 0 , 1 ) {L_0}(0,1) (or L p {L_p} for 0 > p > 1 0 > p > 1 ) which is rigid, i.e. such that every endomorphism in the space is a multiple of the identity.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

1. Non-negative random measures and order-preserving embeddings;Garling, D. J. H.;J. London Math. Soc. (2),1975

2. Linear operators on 𝐿_{𝑝} for 0<𝑝<1;Kalton, N. J.;Trans. Amer. Math. Soc.,1980

3. \bysame, Sequences of random variables in 𝐿_{𝑝} for 0<𝑝<1 (to appear).

4. Quotients of 𝐿_{𝑝}(0,1) for 0≤𝑝<1;Kalton, N. J.;Studia Math.,1979

5. Stable laws and the imbedding of 𝐿^{𝑝} spaces;Kanter, Marek;Amer. Math. Monthly,1973

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