Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multipliers and essential norm on the Drury-Arveson space


Authors: Quanlei Fang and Jingbo Xia
Journal: Proc. Amer. Math. Soc. 139 (2011), 2497-2504
MSC (2010): Primary 47B10, 47B32, 47B38
Published electronically: December 16, 2010
Corrigendum: Proc. Amer. Math. Soc. 141 (2013), 363-368
MathSciNet review: 2784815
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that for multipliers $ f$ of the Drury-Arveson space $ H_{n}^{2}$, $ \Vert f\Vert _{\infty}$ does not dominate the operator norm of $ M_{f}$. We show that in general $ \Vert f\Vert _{\infty}$ does not even dominate the essential norm of $ M_{f}$. A consequence of this is that there exist multipliers $ f$ of $ H_{n}^{2}$ for which $ M_f$ fails to be essentially hyponormal; i.e., if $ K$ is any compact, self-adjoint operator, then the inequality $ M_f^\ast M_f - M_fM_f^\ast + K \geq 0$ does not hold.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47B10, 47B32, 47B38

Retrieve articles in all journals with MSC (2010): 47B10, 47B32, 47B38


Additional Information

Quanlei Fang
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: fangquanlei@gmail.com

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: jxia@acsu.buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10680-9
PII: S 0002-9939(2010)10680-9
Keywords: Multiplier, Drury-Arveson space
Received by editor(s): April 11, 2010
Received by editor(s) in revised form: July 1, 2010
Published electronically: December 16, 2010
Communicated by: Richard Rochberg
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.