A non-hyponormal operator generating Stieltjes moment sequences

详细信息	查看全文 | 推荐本文 |

• 作者：Zenon Jan Jabł ; oń ; ski^a ; ^{Zenon.Jablonski@im.uj.edu.pl} ; Il Bong Jung^b ; ^{ibjung@knu.ac.kr} ; Jan Stochel^a ; ^{Jan.Stochel@im.uj.edu.pl}
• 关键词：Indeterminate moment problem ; N-extremal measure ; Krein and Friedrichs measures ; Directed tree ; Weighted shift on a directed tree ; Hyponormal operator ; Operator generating Stieltjes moment sequences ; Composition operator in an L2-space
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 May, 2012
• 卷：262
• 期：9
• 页码：3946-3980
• 文件大小：298 K

摘要

A linear operator S in a complex Hilbert space for which the set of its -vectors is dense in and is a Stieltjes moment sequence for every is said to generate Stieltjes moment sequences. It is shown that there exists a closed non-hyponormal operator S which generates Stieltjes moment sequences. What is more, is a core of any power of S. This is established with the help of a weighted shift on a directed tree with one branching vertex. The main tool in the construction comes from the theory of indeterminate Stieltjes moment sequences. As a consequence, it is shown that there exists a non-hyponormal composition operator in an -space (over a 蟽-finite measure space) which is injective, paranormal and which generates Stieltjes moment sequences. The independence assertion of Barry Simon始s theorem which parameterizes von Neumann extensions of a closed real symmetric operator with deficiency indices is shown to be false.