Hostname: page-component-7dd5485656-glrdx Total loading time: 0 Render date: 2025-10-30T04:37:46.453Z Has data issue: false hasContentIssue false
  • English
  • Français

Local left invertibility for operator tuples and noncommutative localizations

Published online by Cambridge University Press:  04 September 2008

Anar Dosiev
Anar Dosiev
Affiliation:
Middle East Technical University NCC, Guzelyurt KKTC Mersin 10, Turkey, dosiev@yahoo.com.
Get access

Abstract

In the paper we propose an operator approach to the noncommutative Taylor localization problem based on the local left invertibility for operator tuples acting on a Fréchet space. We prove that the canonical homomorphism of the universal enveloping algebra of a nilpotent Lie algebra into its Arens-Michael envelope is the Taylor localization whenever has normal growth.

Keywords

Arens-Michael envelopenoncommutative localizationentire functions in elements of a nilpotent Lie algebrahomological dimensions

Information

Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 163 - 191
Copyright
Copyright © ISOPP 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Cartan, H., Eilenberg, S., Homological algebra, Princeton Univ. Press, (1956)Google Scholar
2.Dixmier, J., Algèbres enveloppantes, Gauthier-Villars Edit. Paris (1974)Google Scholar
3.Dosiev, A. A., Holomorphic functions of a basis of a nilpotent Lie algebra, Funct. Anal. and its Appl. 34 (4) (2000), 302-304CrossRefGoogle Scholar
4.Dosiev, A. A., Spectra of infinite parametrized Banach complexes, J. Operator Theory 48 (3) (2002), 585-614Google Scholar
5.Dosiev, A. A., Homological dimensions of the algebra formed by entire functions of elements of a nilpotent Lie algebra, Funct. Anal., and its Appl. 37 (1) (2003), 61-64CrossRefGoogle Scholar
6.Dosiev, A. A., Algebras of power series of elements of a Lie algebra and Slodkowski spectra, J. Math. Sciences 124 (2) (2004), 4886-4908 (translated from Zapiski POMI)CrossRefGoogle Scholar
7.Dosiev, A. A., Fréchet algebra sheaf cohomology and spectral theory, Funct. Anal. and its Appl. 39 (3) (2005), 225-228CrossRefGoogle Scholar
8.Dosiev, A. A., Cartan-Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems, J. Funct. Anal. 230 (2006), 446-493CrossRefGoogle Scholar
9.Dosiev, A. A., Quasispectra of solvable Lie algebra homomorphisms into Banach algebras, Stud. Math. 174 (1) (2006), 13-27CrossRefGoogle Scholar
10.Dosiev, A. A., Noncommutative holomorphic functions in elements of a Lie algebra and the absolute basis problem, Izvestiya Math..RAN, (2009) (to appear)CrossRefGoogle Scholar
11.Dosiev, A. A., Formally-radical functions in elements of a nilpotent Lie algebra and noncommutative localizations, Algebra Colloquium (to appear)Google Scholar
12.Eschmeier, J., Putinar, M., Spectral decomposition and Analytic sheaves, Clarendon Press, Oxford, 1996CrossRefGoogle Scholar
13.Fainshtein, A. S., Taylor joint spectrum for families of operators generating nilpotent Lie algebra, J. Operator Theory 29 (1993), 3-27Google Scholar
14.Helemskii, A. Ya., The homology of Banach and topological algebras, Kluwer Academic Publ., V. 41, 1989CrossRefGoogle Scholar
15.Helemskii, A. Ya., Banach and polynormed algebras: general theory, representations, homology, Nauka, Moscow, 1989 (Russian)Google Scholar
16.Meyer, R., Embeddings of derived categories of bornological modules, Preprint (arXiv:math.FA/0410596v1)Google Scholar
17.Neeman, A., Ranicki, A., Noncommutative localization and chain complexes I. Algebraic K- and L-theory, Preprint (arXiv:math.RA/0109118)Google Scholar
18.Pirkovskii, A. Yu., Stably flat completions of universal enveloping algebras, Dissertationes Math. (441) 5-56 (2006) (arXiv:math.FA/0311492v2)CrossRefGoogle Scholar
19.Pirkovskii, A. Yu., Arens-Michael enveloping algebras and analytic smash products, Proc. Amer. Math. Soc. 134 (9) (2006), 2621-2631CrossRefGoogle Scholar
20.Taylor, J. L., Homology and cohomology for topological algebras, Adv. Math. 9 (1972), 137-182CrossRefGoogle Scholar
21.Taylor, J. L., A general framework for a multi-operator functional calculus, Adv. Math. 9 (1972), 183-252CrossRefGoogle Scholar
22.Turovskii, Yu. V., On spectral properties of elements of normed algebras and invariant subspaces, Funktsional. Anal. i Prilozhen. 18 (2) (1984), 77-78CrossRefGoogle Scholar