A+ CATEGORY SCIENTIFIC UNIT

Ordered analytic Hilbert spaces over the unit disk

Volume 185 / 2008

Shengzhao Hou, Shuyun Wei Studia Mathematica 185 (2008), 127-142 MSC: 46E22, 47B32. DOI: 10.4064/sm185-2-2

Abstract

Let $f$, $g$ be in the analytic function ring ${\rm Hol}({\mathbb D})$ over the unit disk ${\mathbb D}$. We say that $f\preceq g$ if there exist $M>0$ and $0< r< 1$ such that $|f(z)|\leq M|g(z)|$ whenever $r< |z|< 1$. Let $X$ be a Hilbert space contained in ${\rm Hol}({\mathbb D})$. Then $X$ is called an ordered Hilbert space if $f\preceq g$ and $g\in X$ imply $f\in X$. In this note, we mainly study the connection between an ordered analytic Hilbert space and its reproducing kernel. We also consider when an invariant subspace of the whole space $X$ is similar to $X$.

Authors

  • Shengzhao HouDepartment of Mathematics
    Suzhou University
    Suzhou, Jiangsu, 215006, P.R. China
    e-mail
  • Shuyun WeiDepartment of Mathematics
    Suzhou University
    Suzhou, Jiangsu, 215006, P.R. China
    e-mail

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