Let 𝕬 be a C*-algebra with identity and real rank zero. Suppose a complex- valued function is holomorphic and bounded on the intersection of the open unit ball of 𝕬 and the identity component of the set of invertible elements of 𝕬. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of 𝕬. The author previously deduced this from a more general fact about Banach algebras.
Digital Object Identifier (DOI)
Harris, Lawrence A., "Removable Singularities in C*-Algebras of Real Rank Zero" (2017). Mathematics Faculty Publications. 38.