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arXiv · 1804.03456

Some remarks about disjointly homogeneous symmetric spaces

S. Astashkin
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Abstract

Let $1\le p<\infty$. A symmetric space $X$ on $[0,1]$ is said to be $p$-disjointly homogeneous (resp. restricted $p$-disjointly homogeneous) if every sequence of normalized pairwise disjoint functions from $X$ (resp. characteristic functions) contains a subsequence equivalent in $X$ to the unit vector basis of $l_p$. Answering a question posed recently, we construct, for each $1\le p<\infty$, a restricted $p$-disjointly homogeneous symmetric space, which is not $p$-disjointly homogeneous. Moreover, we prove that the property of $p$-disjoint homogeneity is preserved under Banach isomorphisms.

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S. Astashkin. 2019-03-17. Some remarks about disjointly homogeneous symmetric spaces. https://doi.org/10.1007/s13163-018-0289-y

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