Tohoku Mathematical Journal
2023
December
SECOND SERIES VOL. 75, NO. 4

Tohoku Math. J.
75 (2023), 465-482

Title INVARIANT STRUCTURE PRESERVING FUNCTIONS AND AN OKA-WEIL KAPLANSKY DENSITY TYPE THEOREM

Author James Eldred Pascoe

(Received April 19, 2021, revised February 24, 2022)
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.

Mathematics Subject Classification. Primary 46L52; Secondary 47A15.
Key words and phrases. Noncommutative function theory, invariant structure preserving functions, Oka-Weil theorem, Kaplansky density theorem.

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