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.

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Published in Journal of Mathematical Analysis and Applications, v. 445, issue 2, p. 1390-1393.

Β© 2016 Elsevier Inc. All rights reserved.

This manuscript version is made available under the CC‐BY‐NC‐ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/.

The document available for download is the author's post-peer-review final draft of the article.

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