On the Algebra Generated by a Poly-Bergman Projection and a Composition Operator

Josue Ramírez () and Ilya M. Spitkovsky ()
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Josue Ramírez: Universidad Autónoma Metropolitana
Ilya M. Spitkovsky: College of William & Mary

A chapter in Factorization, Singular Operators and Related Problems, 2003, pp 273-289 from Springer

Abstract: Abstract Let G be a bounded domain in ℂ with smooth boundary, and let α be a C 2-diffeomorphism of % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaacuWGhbWrgaqeaaaa!309E! $$ \bar{G} $$ such that % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaacqaHXoqycqaH-oWBcqaHXoqycqGH9aqpcq % WGPbqAcqWGKbazdaWgaaWcbaGafm4raCKbaebaaeqaaaaa!3975! $$ \alpha o\alpha = i{{d}_{{\bar{G}}}} $$ . A symbol algebra is described for the C*-algebra generated by a poly-Bergman projection of G, all multiplication operators % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabdggaHjabdMeajjabcI % caOiabdggaHjabgIGiolabdoeadjabcIcaOiqbdEeahzaaraGaeiyk % aKIaeiykaKcaaa!3A66! $$ aI(a \in C(\bar{G})) $$ and the composition operator % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9 % q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir % -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa % aeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabdEfaxjabdAgaMjabg2 % da9iabdAgaMjabgclaWkabeg7aHbaa!3801! $$ Wf = f^\circ \alpha $$ .

Keywords: Bergman projection; composition operator; symbol algebra; factorization; Fredholm operator. (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0227-0_18

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DOI: 10.1007/978-94-017-0227-0_18

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