Abstract:
A problem on noncommutative holomorphic functional calculus is considered for a Banach module over a finite-dimensional nilpotent Lie algebra. As the main result, the transversality property of algebras of noncommutative holomorphic functions with respect to the Taylor spectrum is established for a family of bounded linear operators generating a Heisenberg algebra.
Bibliography: 25 titles.
Keywords:
holomorphic function of elements of a Lie algebra, Taylor spectrum, transversality property, inverting the Fréchet completion.
\Bibitem{Dos10}
\by A.~A.~Dosi
\paper The Taylor spectrum and transversality for a~Heisenberg algebra of operators
\jour Sb. Math.
\yr 2010
\vol 201
\issue 3
\pages 355--375
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https://doi.org/10.1070/SM2010v201n03ABEH004076
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This publication is cited in the following 4 articles:
O. Yu. Aristov, “Razlozhenie algebry analiticheskikh funktsionalov na svyaznoi kompleksnoi gruppe Li i ee popolnenii v iterirovannye analiticheskie smesh-proizvedeniya”, Algebra i analiz, 36:4 (2024), 1–37
Anar Dosi, “Noncommutative Localizations of Lie-Complete Rings”, Communications in Algebra, 44:11 (2016), 4892
A. Dosi, “Noncommutative affine spaces and Lie-complete rings”, C. R. Math. Acad. Sci. Paris, 353:2 (2015), 149–153
A. Dosi, “Taylor functional calculus for supernilpotent Lie algebra of operators”, J. Operator Theory, 63:1 (2010), 191–216
Citation in format AMSBIB
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