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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2010 Volume 201, Number 3, Pages 39–62 (Mi sm7306)

This article is cited in 4 papers

The Taylor spectrum and transversality for a Heisenberg algebra of operators

A. A. Dosi

Middle East Technical University Northern Cyprus Campus

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.

UDC: 517.984.22

MSC: Primary 46H30, 17B30; Secondary 17B35

Received: 02.10.2008 and 14.10.2009

DOI: 10.4213/sm7306


 English version:
Sbornik: Mathematics, 2010, 201:3, 355–375

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