Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 51
Spectrum of Banach-valued holomorphic functions
Zakaria Taki, Abdelkrim Nokrane
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
December 23, 2021
March 03, 2056
April 15, 2056

Abstract: Let A be an unital complex Banach algebra and D be a non empty open domain in the complex plan C. Let f be a holomorphic function from D into A. We set: Σ(f) = f−1(Sing(A)), where Sing(A) is the set of non invertible elements in A.
 In this talk, we give a description of Σ(f) using the classical spectrum of f(z) (z ∈ D). Moreover, we give a partial positive answer to the following problem which was posed by B. Aupetit: If the usual spectrum σ(f(z)) is polar for all z ∈ D, is it true that Σ(f) is polar?