A Note on Values of Noncommutative Polynomials

Abstract

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.

4 pages

References in corpus (2)

• Connes' embedding conjecture and sums of hermitian squares
• Values of Noncommutative Polynomials, Lie Skew-Ideals and the Tracial Nullstellensatz

Cited by in corpus (2)

• The images of multilinear and semihomogeneous polynomials on the algebra of octonions
• Images of multilinear graded polynomials on upper triangular matrix algebras