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Operator identities for standard weighted bergman shift and toeplitz operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)In: Journal of operator theory, ISSN 0379-4024, E-ISSN 1841-7744, Vol. 70, no 2, 451-475 p.Article in journal (Refereed) Published
Abstract [en]

We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator inequalities and structure formulas for reproducing kernel functions which make contact with work of Richter, Shimorin, and others.

Place, publisher, year, edition, pages
2013. Vol. 70, no 2, 451-475 p.
Keyword [en]
Bergman space, Functional calculus, Reproducing kernel function, Shift operator, Toeplitz operator
National Category
URN: urn:nbn:se:kth:diva-139445DOI: 10.7900/jot.2011sep09.1967ISI: 000330815600006ScopusID: 2-s2.0-84889649765OAI: diva2:688372

QC 20140116

Available from: 2014-01-16 Created: 2014-01-13 Last updated: 2014-03-06Bibliographically approved

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