## Abstract

Let T be a cyclic subnormal operator on a Hilbert space ℋ with cyclic vector x_{0} and let γ_{ij}:=(T*^{i}T ^{j}x_{0},x_{0}), for any i,j ∈ ℕ ∪ {0}. The Bram-Halmos' characterization for subnormality of T involved a moment matrix M(n). In a parallel approach, we construct a moment matrix E(n) corresponding to Embry's characterization for subnormality of T. We discuss the relationship between M(n) and E(n) via the full moment problem. Next, given a collection of complex numbers γ≡{γ_{ij}} (0 ≤ i + j ≤ 2n, |i-j| ≤ n) with γ_{00} > 0 and γ _{ji} = γ̄_{ij}, we consider the truncated complex moment problem for γ; this entails finding a positive Borel measure μ supported in the complex plane ℂ such that γ_{ij} = ∫z̄^{i}z^{j}dμ(z). We show that this moment problem can be solved when E(n) ≥ 0 and E(n) admits a flat extension E(n + k), where k = 1 when n is odd and k = 2 when n is even.

Original language | English |
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Pages (from-to) | 95-114 |

Number of pages | 20 |

Journal | Linear Algebra and Its Applications |

Volume | 375 |

Issue number | 1-3 |

DOIs | |

State | Published - 1 Dec 2003 |

### Bibliographical note

Funding Information:The authors would like to express their gratitude to the referee for valuable comments. This work was supported by Korea Research Foundation Grant (KRF-2002-070-C00006).

## Keywords

- Cyclic subnormal operators
- Truncated complex moment problem
- k-Hyponormal operator