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dc.contributor.authorKaptanoğlu, H. T.en_US
dc.date.accessioned2016-02-08T11:02:40Z
dc.date.available2016-02-08T11:02:40Z
dc.date.issued2014en_US
dc.identifier.issn0219-1997
dc.identifier.urihttp://hdl.handle.net/11693/26637
dc.description.abstractWe obtain all Dirichlet spaces Fq, q ∈ ℝ, of holomorphic functions on the unit ball of ℂN as weighted symmetric Fock spaces over ℂN. We develop the basics of operator theory on these spaces related to shift operators. We do a complete analysis of the effect of q ∈ ℝ in the topics we touch upon. Our approach is concrete and explicit. We use more function theory and reduce many proofs to checking results on diagonal operators on the Fq. We pick out the analytic Hilbert modules from among the Fq. We obtain von Neumann inequalities for row contractions on a Hilbert space with respect to each Fq. We determine the commutants and investigate the almost normality of the shift operators. We prove that the C∗-algebras generated by the shift operators on the Fq fit in exact sequences that are in the same Ext class. We identify the groups K0 and K1 of the Toeplitz algebras on the Fq arising in K-theory. Radial differential operators are prominent throughout. Some of our results, especially those pertaining to lower negative values of q, are new even for N = 1. Many of our results are valid in the more general weighted symmetric Fock spaces Fb that depend on a weight sequence b. © World Scientific Publishing Company.en_US
dc.language.isoEnglishen_US
dc.source.titleCommunications in Contemporary Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1142/S021919971350034Xen_US
dc.subjectAnalytic Hilbert moduleen_US
dc.subjectBergmanen_US
dc.subjectBusby invarianten_US
dc.subjectCommutanten_US
dc.subjectC∗-algebraen_US
dc.subjectDirichleten_US
dc.subjectDrury-Arvesonen_US
dc.subjectExtensionen_US
dc.subjectFocken_US
dc.subjectFredholmen_US
dc.subjectHardyen_US
dc.subjecthyponormalen_US
dc.subjectK-groupsen_US
dc.subjectmultiplieren_US
dc.subjectRadial differential operatoren_US
dc.subjectReproducing kernel Hilbert spaceen_US
dc.subjectRow contractionen_US
dc.subjectShiften_US
dc.subjectShort exact sequenceen_US
dc.subjectSpectrumen_US
dc.subjectSubnormalen_US
dc.subjectToeplitzen_US
dc.subjectVirtual pointen_US
dc.subjectVvon Neumann inequalityen_US
dc.subject47A13en_US
dc.subject47B32en_US
dc.subject19K33en_US
dc.subject32A36en_US
dc.subject32A37en_US
dc.subject46E20en_US
dc.subject46E22en_US
dc.subject46L08en_US
dc.subject47A20en_US
dc.subject47A30en_US
dc.subject47A53en_US
dc.subject47B35en_US
dc.subject47B37en_US
dc.subject47B38en_US
dc.subject47C15en_US
dc.titleAspects of multivariable operator theory on weighted symmetric Fock spacesen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage1350034-1en_US
dc.citation.epage1350034-49en_US
dc.citation.volumeNumber16en_US
dc.citation.issueNumber5en_US
dc.identifier.doi10.1142/S021919971350034Xen_US
dc.publisherWorld Scientific Publishingen_US
dc.identifier.eissn1793-6683


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