TL;DR
This paper refines the non-commutative Oka-Weil theorem by characterizing free compact nc sets through dilation hulls, enabling free holomorphic functions to be approximated by free polynomials.
Contribution
It introduces a new characterization of free compact nc sets using dilation hulls, enhancing the approximation of free holomorphic functions.
Findings
Free holomorphic functions can be represented as free polynomials on free compact nc sets.
The refinement provides a new approach to the nc Oka-Weil theorem.
Characterization of free compact nc sets via dilation hulls is established.
Abstract
This short note refines nc Oka-Weil theorem by using a characterization of free compact nc sets based on the notion of dilation hulls. A consequence of it is that any free holomorphic function can be represented as a free polynomial on each free compact nc set.
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