A Note on Values of Noncommutative Polynomials
classification
🧮 math.OA
math.RA
keywords
algebrasclassnoncommutativevaluesboundedcompactdimensionalequals
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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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