Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem. (English) Zbl 1541.46044
Summary: 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 approximable 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.
MathOverflow Questions:
The ball formulation of the Kaplansky density theorem in nonselfadjoint algebrasMSC:
| 46L52 | Noncommutative function spaces |
| 47A15 | Invariant subspaces of linear operators |
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
Keywords:
invariant structure preserving functions; Kaplansky density theorem; noncommutative function theory; Oka-Weil theorem; free functionsSoftware:
MathOverflowReferences:
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