A Note on Values of Noncommutative Polynomials
Matej Bresar, Igor Klep

TL;DR
This paper identifies a class of algebras where every nontrivial noncommutative polynomial's values span the entire algebra, including bounded and compact operators on infinite-dimensional Hilbert spaces.
Contribution
It introduces a class of algebras with the property that polynomial values are dense, expanding understanding of polynomial identities in operator algebras.
Findings
Algebras where polynomial values span the entire algebra
Includes all bounded and compact operators on infinite-dimensional Hilbert spaces
Provides insight into polynomial identities in operator algebras
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.
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