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The common range of co-analytic Toeplitz operators on the Drury-Arveson space

Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan (2023) In Journal d'Analyse Mathematique 150(1). p.215-247
Abstract

We characterize the common range of the adjoints of cyclic multiplication operators on the Drury-Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition. To achieve this, we introduce the uniform Smirnov class on the ball and determine its dual space. We show that the dual space of the uniform Smirnov class equals the dual space of the strictly smaller Smirnov class of the Drury-Arveson space, and that this in turn equals the common range of the adjoints of cyclic multiplication operators.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal d'Analyse Mathematique
volume
150
issue
1
pages
215 - 247
publisher
Magnes Press
external identifiers
  • scopus:85145669432
ISSN
0021-7670
DOI
10.1007/s11854-022-0265-9
language
English
LU publication?
yes
id
89fb46e7-6b03-48bb-b672-dd47936b04b4
date added to LUP
2023-02-13 09:16:59
date last changed
2023-10-26 14:52:00
@article{89fb46e7-6b03-48bb-b672-dd47936b04b4,
  abstract     = {{<p>We characterize the common range of the adjoints of cyclic multiplication operators on the Drury-Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition. To achieve this, we introduce the uniform Smirnov class on the ball and determine its dual space. We show that the dual space of the uniform Smirnov class equals the dual space of the strictly smaller Smirnov class of the Drury-Arveson space, and that this in turn equals the common range of the adjoints of cyclic multiplication operators.</p>}},
  author       = {{Aleman, Alexandru and Hartz, Michael and McCarthy, John E. and Richter, Stefan}},
  issn         = {{0021-7670}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{215--247}},
  publisher    = {{Magnes Press}},
  series       = {{Journal d'Analyse Mathematique}},
  title        = {{The common range of co-analytic Toeplitz operators on the Drury-Arveson space}},
  url          = {{http://dx.doi.org/10.1007/s11854-022-0265-9}},
  doi          = {{10.1007/s11854-022-0265-9}},
  volume       = {{150}},
  year         = {{2023}},
}