Ordered analytic Hilbert spaces over the unit disk

Shengzhao Hou, and Shuyun Wei. "Ordered analytic Hilbert spaces over the unit disk." Studia Mathematica 185.2 (2008): 127-142. <http://eudml.org/doc/286215>.

@article{ShengzhaoHou2008,
abstract = {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.},
author = {Shengzhao Hou, Shuyun Wei},
journal = {Studia Mathematica},
keywords = {analytic Hilbert space; ordered analytic Hilbert space},
language = {eng},
number = {2},
pages = {127-142},
title = {Ordered analytic Hilbert spaces over the unit disk},
url = {http://eudml.org/doc/286215},
volume = {185},
year = {2008},
}

TY - JOUR
AU - Shengzhao Hou
AU - Shuyun Wei
TI - Ordered analytic Hilbert spaces over the unit disk
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 2
SP - 127
EP - 142
AB - 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.
LA - eng
KW - analytic Hilbert space; ordered analytic Hilbert space
UR - http://eudml.org/doc/286215
ER -