A note on values of noncommutative polynomials
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- by Matej Brešar and Igor Klep PDF
- Proc. Amer. Math. Soc. 138 (2010), 2375-2379 Request permission
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.References
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Additional Information
- Matej Brešar
- 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, Koroška 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, Koroška 160, SI-2000 Maribor, Slovenia
- Email: igor.klep@fmf.uni-lj.si
- Received by editor(s): September 30, 2009
- Received by editor(s) in revised form: December 2, 2009
- Published electronically: 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 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2375-2379
- MSC (2010): Primary 08B20, 16R99, 47L30
- DOI: https://doi.org/10.1090/S0002-9939-10-10324-4
- MathSciNet review: 2607866