On the full range of Zippin and inclusion indices of rearrangement-invariant spaces,Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

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On the full range of Zippin and inclusion indices of rearrangement-invariant spaces
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2024-04-17 , DOI: 10.1007/s13398-024-01599-8
Guillermo P. Curbera , Oleksiy Karlovych , Eugene Shargorodsky

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 \(\gamma _X=\gamma \), \(\delta _X=\delta \).

更新日期：2024-04-18

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