Journal of Operator Theory

Volume 84, Issue 2, Fall 2020 pp. 365-367.

An entire free holomorphic function which is unbounded on the row ball

Authors: J.E. Pascoe
Author institution: Department of Mathematics, 1400 Stadium Rd, University of Florida, Gainesville, FL 32611, U.S.A.

Summary: We give an entire free holomorphic function $f$ which is unbounded on the row ball. That is, we give a holomorphic free noncommutative function which is continuous in the free topology developed by Agler and McCarthy but is unbounded on the set of row contractions.

DOI: http://dx.doi.org/10.7900/jot.2019jun05.2242
Keywords: free topology, row ball, noncommutative function theory

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