Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON STAR MOMENT SEQUENCE OF OPERATORS

  • Park, Sun-Hyun (Department of Mathematics, Kyungpook National University)
  • Received : 2007.08.08
  • Accepted : 2007.10.06
  • Published : 2007.12.25
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Abstract

Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\cal{T}$ acting on $\cal{H}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\cal{H}$ and a positive Borel measure ${\mu}$ such that <$T^{*j}T^ku$, v> = ${^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu$ for all j, $k\;\geq\;0$. We obtain a characterization to find a representing star moment measure and discuss some related properties.

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References

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