A non-hyponormal operator generating Stieltjes moment sequences
2014.03.24 19:21
| 실적년도 | 2011 년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Il Bong Jung, Z. Jab Il Bong Jung |
| 학술지명 | Journal of Functional Analysis |
| 권(Vol.) | 262 |
| 호(No.) | 9 |
| 게재년월 | 년 월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
A linear operator S in a complex Hilbert space H for which the set D∞(S) of its C∞-vectors is dense in H and {Snf 2}∞ n0 is a Stieltjes moment sequence for every f ∈ D∞(S) 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, D∞(S) is a core of any power Sn 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 L2-space (over a σ-finite measure space) which is injective, paranormal and which generates Stieltjes moment sequences. The independence assertion of Barry Simon’s theorem which parameterizes von Neumann extensions of a closed real symmetric operator with deficiency indices (1, 1) is shown to be false.
