Abstract
Let be a complex unital Banach algebra and D be a non-empty open connected subset of Let f be a holomorphic -valued function on D. We set: where is the set of all invertible elements in . In this paper, we give a description of using the classical spectrum of . Moreover, within the framework of this paper, we give a partial positive answer to the following problem which was posed by B. Aupetit: If the usual spectrum is polar for all is it true that is polar?
Acknowledgments
The authors would like to express their sincere gratitude to the referee for his careful review of this paper, valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).