On the full range of Zippin and inclusion indices of rearrangement-invariant spaces

Eugene Shargorodsky, Guillermo P. Curbera, Oleksiy Karlovych*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let $X$ be a rearrangement-invariant space on $[0,1]$. It is known that its Zippin indices $\underline{\beta}{}_X,\overline{\beta}{}_X$ and
its inclusion indices $\gamma_X,\delta_X$ are related as follows:
$0\le\underline{\beta}{}_X\le 1/\gamma_X
\le
1/\delta_X\le\overline{\beta}{}_X\le 1$.
We show that given $\underline{\beta},\overline{\beta}\in[0,1]$
and $\gamma,\delta\in[1,\infty]$ satisfying
$\underline{\beta}\le 1/\gamma\le 1/\delta\le \overline{\beta}$, there
exists a rearrangement-invariant space $X$ such that
$\underline{\beta}{}_X=\underline{\beta}$,
$\overline{\beta}{}_X=\overline{\beta}$
and $\gamma_X=\gamma$, $\delta_X=\delta$.
Original languageEnglish
Article number93
Number of pages17
JournalRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Volume118
Early online date17 Apr 2024
Publication statusE-pub ahead of print - 17 Apr 2024

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