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

Abstract

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.

Locations

• Tohoku Mathematical Journal - View
• arXiv (Cornell University) - View - PDF
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