Multipliers and essential norm on the drury-arveson space

Quanlei Fang; Jingbo Xia

doi:10.1090/S0002-9939-2010-10680-9

Multipliers and essential norm on the drury-arveson space

Quanlei Fang
, Jingbo Xia

Mathematics

SUNY Buffalo

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

It is well known that for multipliers f of the Drury-Arveson space H ²_n,||f||∞ does not dominate the operator norm of Mf . We show that in general ||f||∞ does not even dominate the essential norm ofMf . A consequence of this is that there exist multipliers f of H ²_n for whichMf fails to be essentially hyponormal; i.e., if K is any compact, self-adjoint operator, then the inequality M*_fM_f -M_fM*_f + K ≥ 0 does not hold.

Original language	English
Pages (from-to)	2497-2504
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-2010-10680-9
State	Published - Jul 2011

Keywords

Drury-Arveson space
Multiplier

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10.1090/S0002-9939-2010-10680-9

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abstract = "It is well known that for multipliers f of the Drury-Arveson space H 2n,||f||∞ does not dominate the operator norm of Mf . We show that in general ||f||∞ does not even dominate the essential norm ofMf . A consequence of this is that there exist multipliers f of H 2n for whichMf fails to be essentially hyponormal; i.e., if K is any compact, self-adjoint operator, then the inequality M*fMf -MfM*f + K ≥ 0 does not hold.",

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KW - Multiplier

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ER -

Multipliers and essential norm on the drury-arveson space

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Keywords

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