A. A. Dosi, “Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem”, Izv. RAN. Ser. Mat., 73:6 (2009), 77

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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 6, Pages 77–100 (Mi izv2661)

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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, Güzelyurt

Abstract: We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra $\mathfrak g$. 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.

UDC: 512.556+517.553

MSC: 46H30, 46A35, 17B35

Received: 10.05.2007

Citation: A. A. Dosi, “Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem”, Izv. RAN. Ser. Mat., 73:6 (2009), 77–100

Citation in format AMSBIB:

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\pages 77--100
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\jour Izv. Math.
\yr 2009
\vol 73
\issue 6
\pages 1149--1171
\crossref{http://dx.doi.org/10.1070/IM2009v073n06ABEH002476}
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Full text (in Russian): PDF file (615 kB)

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English version:
Izvestiya: Mathematics, 2009, 73:6, 1149–1171

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ISI Web of Knowledge: 000274926100004

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:

А. А. Доси, “Спектр Тейлора и трансверсальность для операторной алгебры Гейзенберга”, Матем. сб., 201:3 (2010), 39–62 ; A. A. Dosi, “The Taylor spectrum and transversality for a Heisenberg algebra of operators”, Sb. Math., 201:3 (2010), 355–375

Известия Российской академии наук. Серия математическая

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