# Ordered analytic Hilbert spaces over the unit disk

Studia Mathematica (2008)

- Volume: 185, Issue: 2, page 127-142
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topShengzhao 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.