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Transactions of the American Mathematical Society

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Ideals in a multiplier algebra on the ball


Authors: Raphaël Clouâtre and Kenneth R. Davidson
Journal: Trans. Amer. Math. Soc. 370 (2018), 1509-1527
MSC (2010): Primary 46J20, 46E22
DOI: https://doi.org/10.1090/tran/7007
Published electronically: November 22, 2017
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Abstract: We study the ideals of the closure of the polynomial multipliers on the Drury-Arveson space. Structural results are obtained by investigating the relation between an ideal and its weak-$ *$ closure, much in the spirit of the corresponding classical facts for the disc algebra. Zero sets for multipliers are also considered and are deeply intertwined with the structure of ideals. Our approach is primarily based on duality arguments.


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Additional Information

Raphaël Clouâtre
Affiliation: Department of Mathematics, University of Manitoba, 186 Dysart Road, Winnipeg, Manitoba, Canada R3T 2N2
Email: raphael.clouatre@umanitoba.ca

Kenneth R. Davidson
Affiliation: Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1
Email: krdavids@uwaterloo.ca

DOI: https://doi.org/10.1090/tran/7007
Keywords: Ideals, zero sets, ball algebra, multipliers, Drury-Arveson space
Received by editor(s): April 18, 2016
Published electronically: November 22, 2017
Additional Notes: The first author was partially supported by an FQRNT postdoctoral fellowship and a start-up grant from the University of Manitoba.
The second author was partially supported by an NSERC grant.
Article copyright: © Copyright 2017 American Mathematical Society

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