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Izvestiya: Mathematics, 2009, Volume 73, Issue 6, Pages 1149–1171
DOI: https://doi.org/10.1070/IM2009v073n06ABEH002476 (Mi im2661) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem

A. A. Dosi

Middle East Technical University Northern Cyprus Campus
English version PDF (378 kB) Citations (12) Russian version article
References:
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DOI: https://doi.org/10.1070/IM2009v073n06ABEH002476
Abstract: We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.
Keywords: holomorphic functions in elements of a Lie algebra, Arens–Michael envelope, localization.
Received: 10.05.2007
Bibliographic databases:
UDC: 512.556+517.553
MSC: 46H30, 46A35, 17B35
Language: English
Original paper language: Russian
Citation: A. A. Dosi, “Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem”, Izv. Math., 73:6 (2009), 1149–1171
Citation in format AMSBIB
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\vol 73
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Linking options:
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  • https://doi.org/10.1070/IM2009v073n06ABEH002476
  • https://www.mathnet.ru/eng/im/v73/i6/p77
    • This publication is cited in the following 12 articles:
    1. A. Dosi, “Algebraic spectral theory and the Serre multiplicity formula”, Algebra i analiz, 37:1 (2025), 57–103  mathnet
    2. M. Yu. Dmitrieva, “Bundles of holomorphic function algebras on subvarieties of the noncommutative ball”, Funct. Anal. Appl., 58:3 (2024), 268–288  mathnet  crossref  crossref
    3. Anar Dosi, “The spectrum of a module along scheme morphism and multi-operator functional calculus”, Mosc. Math. J., 21:2 (2021), 287–323  mathnet  crossref
    4. St. Petersburg Math. J., 31:4 (2020), 607–656  mathnet  crossref  isi  elib
    5. Pirkovskii A.Yu., “Holomorphic Functions on the Quantum Polydisk and on the Quantum Ball”, J. Noncommutative Geom., 13:3 (2019), 857–886  crossref  mathscinet  isi  scopus
    6. Dosi A., “Noncommutative Localizations of Lie-Complete Rings”, Commun. Algebr., 44:11 (2016), 4892–4944  crossref  mathscinet  zmath  isi  elib  scopus
    7. Dosi A., “Noncommutative Affine Spaces and Lie-Complete Rings”, C. R. Math., 353:2 (2015), 149–153  crossref  mathscinet  zmath  isi  elib
    8. Pirkovskii A.Yu., “Holomorphically Finitely Generated Algebras”, J. Noncommutative Geom., 9:1 (2015), 215–264  crossref  mathscinet  zmath  isi  elib
    9. A. Yu. Pirkovskii, “Noncommutative analogues of Stein spaces of finite embedding dimension”, Algebraic Methods in Functional Analysis, the Victor Shulman Anniversary Volume, Operator Theory Advances and Applications, 233, eds. Todorov I., Turowska L., 2014, 135–153  crossref  mathscinet  zmath  isi
    10. A. A. Dosi, “The Taylor spectrum and transversality for a Heisenberg algebra of operators”, Sb. Math., 201:3 (2010), 355–375  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Dosi A., “Taylor functional calculus for supernilpotent Lie algebra of operators”, J. Operator Theory, 63:1 (2010), 191–216  mathscinet  zmath  isi
    12. Anar Dosiev, “Local left invertibility for operator tuples and noncommutative localizations”, J K-Theor, 4:1 (2009), 163  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:74
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