## Subspaces of $$L_p$$ for $$0 \leq p < 1$$ that are admissible as kernels.(English)Zbl 1038.46003

For $$L_p=L_p[0,1]$$ spaces, $$0\leqslant p<1$$, the author establishes a condition for a number of subspaces to be admissible as kernels (meaning that such a subspace is a kernel of some continuous linear automorphism on $$L_p$$). Let $$(f_n)$$ be a sequence of independent random variables which generate the full $$\sigma$$-algebra of Borel sets. Then $$\langle f_n\rangle ^\infty _{n=1}$$ is an admissible kernel. It is also shown that if $$X$$ is an admissible kernel, then $$L_p/X$$ is strictly transitive.

### MSC:

 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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