A Note on Values of Noncommutative Polynomials

Details A Note on Values of Noncommutative Polynomials A Note on Values of Noncommutative Polynomials

2009-09-14

arxiv.org/abs/0909.2640v1

Proc. Amer. Math. Soc. 138 (2010), no. 7, 2375-2379

Mathematics

Operator Algebras

4 pages

Scientific paper

10.1090/S0002-9939-10-10324-4

We find a class of algebras A satisfying the following property: for every
nontrivial noncommutative polynomial, the linear span of all its values in A
equals A. This class includes the algebras of all bounded and all compact
operators on an infinite dimensional Hilbert space.

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