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An operator inequality for weighted Bergman shift operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)In: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 29, no 3, 789-808 p.Article in journal (Refereed) Published
Abstract [en]

We prove an operator inequality for the Bergman shift operator on weighted Bergman spaces of analytic functions in the unit disc with weight function controlled by a curvature parameter α assuming nonnegative integer values. This generalizes results by Shimorin, Hedenmalm and Jakobsson concerning the cases α = 0 and α = 1. A naturally derived scale of Hilbert space operator inequalities is studied and shown to be relaxing as the parameter α > -1 increases. Additional examples are provided in the form of weighted shift operators.

Place, publisher, year, edition, pages
2013. Vol. 29, no 3, 789-808 p.
Keyword [en]
Bergman shift operator, Operator inequality, Weighted shift operator
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-133264DOI: 10.4171/RMI/740ISI: 000326990500003Scopus ID: 2-s2.0-84884166371OAI: oai:DiVA.org:kth-133264DiVA: diva2:660361
Note

QC 20131029

Available from: 2013-10-29 Created: 2013-10-29 Last updated: 2017-12-06Bibliographically approved

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