Embry truncated complex moment problem

Il Bong Jung, Eungil Ko, Chunji Li, Sang Soo Park

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let T be a cyclic subnormal operator on a Hilbert space ℋ with cyclic vector x0 and let γij:=(T*iT jx0,x0), 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≡{γij} (0 ≤ i + j ≤ 2n, |i-j| ≤ n) with γ00 > 0 and γ ji = γ̄ij, 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 γij = ∫z̄izjdμ(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 languageEnglish
Pages (from-to)95-114
Number of pages20
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - 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).


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


Dive into the research topics of 'Embry truncated complex moment problem'. Together they form a unique fingerprint.

Cite this