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Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem

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 Added by J E Pascoe
 Publication date 2021
  fields
and research's language is English
 Authors J. E. Pascoe




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We develop the theory of invariant structure preserving and free functions on a general structured topological space. We show that an invariant structure preserving function is pointwise approximiable by the appropriate analog of polynomials in the strong topology and therefore a free function. Moreover, if a domain of operators on a Hilbert space is polynomially convex, the set of free functions satisfies a Oka-Weil Kaplansky density type theorem -- contractive functions can be approximated by contractive polynomials.



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