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Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat."],"published-print":{"date-parts":[[2024,7]]},"abstract":"Abstract<\/jats:title>Let X<\/jats:italic> be a rearrangement-invariant space on [0,\u00a01]. It is known that its Zippin indices $$\\underline{\\beta }{}_X,\\overline{\\beta }{}_X$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n ,<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and its inclusion indices $$\\gamma _X,\\delta _X$$<\/jats:tex-math>\n \n \n \u03b3<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n ,<\/mml:mo>\n \n \u03b4<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are related as follows: $$0\\le \\underline{\\beta }{}_X\\le 1\/\\gamma _X \\le 1\/\\delta _X\\le \\overline{\\beta }{}_X\\le 1$$<\/jats:tex-math>\n \n 0<\/mml:mn>\n \u2264<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n \u2264<\/mml:mo>\n 1<\/mml:mn>\n \/<\/mml:mo>\n \n \u03b3<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n \u2264<\/mml:mo>\n 1<\/mml:mn>\n \/<\/mml:mo>\n \n \u03b4<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n \u2264<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n \u2264<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We show that given $$\\underline{\\beta },\\overline{\\beta }\\in [0,1]$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n ,<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n \u2208<\/mml:mo>\n \n [<\/mml:mo>\n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n ]<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$\\gamma ,\\delta \\in [1,\\infty ]$$<\/jats:tex-math>\n \n \u03b3<\/mml:mi>\n ,<\/mml:mo>\n \u03b4<\/mml:mi>\n \u2208<\/mml:mo>\n [<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n \u221e<\/mml:mi>\n ]<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> satisfying $$\\underline{\\beta }\\le 1\/\\gamma \\le 1\/\\delta \\le \\overline{\\beta }$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n \u2264<\/mml:mo>\n 1<\/mml:mn>\n \/<\/mml:mo>\n \u03b3<\/mml:mi>\n \u2264<\/mml:mo>\n 1<\/mml:mn>\n \/<\/mml:mo>\n \u03b4<\/mml:mi>\n \u2264<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, there exists a rearrangement-invariant space X<\/jats:italic> such that $$\\underline{\\beta }{}_X=\\underline{\\beta }$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n =<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u0332<\/mml:mo>\n <\/mml:munder>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, $$\\overline{\\beta }{}_X=\\overline{\\beta }$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n \n \n X<\/mml:mi>\n <\/mml:msub>\n =<\/mml:mo>\n \n \u03b2<\/mml:mi>\n \u00af<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$\\gamma _X=\\gamma $$<\/jats:tex-math>\n \n \n \u03b3<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n =<\/mml:mo>\n \u03b3<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, $$\\delta _X=\\delta $$<\/jats:tex-math>\n \n \n \u03b4<\/mml:mi>\n X<\/mml:mi>\n <\/mml:msub>\n =<\/mml:mo>\n \u03b4<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s13398-024-01599-8","type":"journal-article","created":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T13:04:57Z","timestamp":1713359097000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the full range of Zippin and inclusion indices of rearrangement-invariant spaces"],"prefix":"10.1007","volume":"118","author":[{"given":"Guillermo P.","family":"Curbera","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6815-0561","authenticated-orcid":false,"given":"Oleksiy","family":"Karlovych","sequence":"additional","affiliation":[]},{"given":"Eugene","family":"Shargorodsky","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,17]]},"reference":[{"issue":"2","key":"1599_CR1","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1090\/S1061-0022-06-00902-2","volume":"17","author":"SV Astashkin","year":"2006","unstructured":"Astashkin, S.V.: On the interpolation of intersections by the real method. 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