Unbounded subnormal weighted shifts on directed trees

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• 作者：Piotr Budzy艅ski^a ; ^{piotr.budzynski@ur.krakow.pl} ; Zenon Jan Jab艂o艅ski^b ; ^{Zenon.Jablonski@im.uj.edu.pl} ; Il Bong Jung^c ; ^{ibjung@knu.ac.kr} ; Jan Stochel^b ; ^{stochelj@hotmail.com} ; ^{Jan.Stochel@im.uj.edu.pl}
• 关键词：Directed tree ; Weighted shift on a directed tree ; Stieltjes moment sequence ; Subnormal operator
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 October, 2012
• 卷：394
• 期：2
• 页码：819-834
• 文件大小：326 K

摘要

A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established. An approach to this issue via consistent systems of probability measures is invented. The role played by determinate Stieltjes moment sequences is elucidated. Lambert鈥檚 characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi-analytic vectors, which is a new phenomenon in this area.