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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10680-9

Published electronically:
December 16, 2010

Corrigendum:
Proc. Amer. Math. Soc. 141 (2013), 363-368

MathSciNet review:
2784815

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Abstract: It is well known that for multipliers of the Drury-Arveson space , does not dominate the operator norm of . We show that in general does not even dominate the essential norm of . A consequence of this is that there exist multipliers of for which fails to be essentially hyponormal; i.e., if is any compact, self-adjoint operator, then the inequality does not hold.

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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:
https://doi.org/10.1090/S0002-9939-2010-10680-9

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.