{"title":"A universal formula for derivation operators and applications","authors":"J. Suárez de la Fuente","doi":"10.1007/s10476-024-00028-7","DOIUrl":null,"url":null,"abstract":"<div><p>We give a universal formula describing derivation operators on a \nHilbert space for a large class of interpolation methods. It is based on a simple new technique on \n“critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in \nparticular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real <i>J</i>-method. Previously, \nsuch space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial \nderivations whose values on the critical points grow to infinity as slowly as we wish.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00028-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-024-00028-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give a universal formula describing derivation operators on a
Hilbert space for a large class of interpolation methods. It is based on a simple new technique on
“critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in
particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real J-method. Previously,
such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial
derivations whose values on the critical points grow to infinity as slowly as we wish.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
