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ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on values of noncommutative polynomials

Author(s): Matej Bresar; Igor Klep
Journal: Proc. Amer. Math. Soc. 138 (2010), 2375-2379.
MSC (2010): Primary 08B20, 16R99, 47L30
Posted: March 15, 2010
MathSciNet review: 2607866
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Abstract | References | Similar articles | Additional information

Abstract: We find a class of algebras $\mathcal{A}$ satisfying the following property: for every nontrivial noncommutative polynomial $f(X_1,\ldots,X_n)$ , the linear span of all its values $f(a_1,\ldots,a_n)$ , $a_i\in \mathcal{A}$ , equals $\mathcal{A}$ . This class includes the algebras of all bounded and all compact operators on an infinite dimensional Hilbert space.

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Additional Information:

Matej Bresar
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia - and - Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, SI-2000 Maribor, Slovenia
Email: matej.bresar@fmf.uni-lj.si

Igor Klep
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia - and - Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, SI-2000 Maribor, Slovenia
Email: igor.klep@fmf.uni-lj.si

DOI: 10.1090/S0002-9939-10-10324-4
PII: S 0002-9939(10)10324-4
Keywords: Noncommutative polynomial, Lie ideal, Hilbert space, bounded operator, compact operator
Received by editor(s): September 30, 2009,
Received by editor(s) in revised form: December 2, 2009
Posted: March 15, 2010
Additional Notes: The first author was supported by the Slovenian Research Agency (program No. P1-0288).
The second author was supported by the Slovenian Research Agency (program No. P1-0222).
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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