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Spectrum of banach valued holomorphic functions and polar sets.
- Source :
- Linear & Multilinear Algebra; 12/31/2022, Vol. 70 Issue 22, p7650-7655, 6p
- Publication Year :
- 2022
-
Abstract
- Let A be a complex unital Banach algebra and D be a non-empty open connected subset of C. Let f be a holomorphic A-valued function on D. We set: ∑(f) = {z ∈ D | f(z) ∉ ∈ Inv(A)}, where Inv(A) is the set of all invertible elements in A. In this paper, we give a description of ∑(f) using the classical spectrum of f(z) (z ∈ D). 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 σ(f(z)) is polar for all z ∈ D, is it true that ∑(f) is polar? [ABSTRACT FROM AUTHOR]
- Subjects :
- SET functions
BANACH algebras
HOLOMORPHIC functions
ANALYTIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 70
- Issue :
- 22
- Database :
- Complementary Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 171945517
- Full Text :
- https://doi.org/10.1080/03081087.2021.2003285