Ordered analytic Hilbert spaces over the unit disk

• Autorzy: Shengzhao Hou , Shuyun Wei
• Języki publikacji: EN

Abstrakty

EN

Let f, g be in the analytic function ring Hol(𝔻) over the unit disk 𝔻. We say that f ⪯ g if there exist M > 0 and 0 < r < 1 such that |f(z)| ≤ M|g(z)| whenever r < |z| < 1. Let X be a Hilbert space contained in Hol(𝔻). Then X is called an ordered Hilbert space if f ⪯ g and g ∈ X imply f ∈ 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.

Kategorie tematyczne

• 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
• 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 2
• Strony: 127-142

Daty

wydano

2008

Twórcy

autor

Shengzhao Hou

• Department of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, P.R. China

autor

Shuyun Wei

• Department of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, P.R. China

Identyfikatory

DOI

10.4064/sm185-2-2