Hardy inequality and the construction of infinitesimal operators with non-basis family of eigenvectors

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• 作者：Grigory M. Sklyar^a ; ^{sklar@univ.szczecin.pl} ; Vitalii Marchenko^b ; ^{v.marchenko@ilt.kharkov.ua}
• 关键词：47D06 ; 34G10 ; 46B45 ; 46B15
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：272
• 期：3
• 页码：1017-1043
• 全文大小：479 K
• 卷排序：272

文摘

Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete Hardy inequality plays an important role in the proposed approach. The construction complements the results of G.Q. Xu et al. (2005) [28] and H. Zwart (2010) [30] on the Riesz basis property of eigenvectors (eigenspaces) of infinitesimal operators. Our results are extended to the case of operators on some Banach spaces.