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- Title
Algebras of Lorch Analytic Mappings Defined on Uniform Algebras.
- Authors
MAURO, Guilherme V. S.; MORAES, Luiza A.
- Abstract
For a unitary commutative complex Banach algebra E, let HL(U) be the space of the mappings from an open connected subset U of E into E that are analytic in the sense of Lorch. We consider the space HL(U) endowed with a convenient topology τd which coincides with the topology τb when U=E or U=Br(z0)={z∈E; ∥z-z0∥<r} (z0∈E, r>0). We consider the case U=EΩ={z∈E; σ(z)⊂Ω} where Ω⊊C is a simply connected domain and we study topological and algebraic properties of (HL(EΩ),τd) for special algebras E. A description of the spectrum of (HL(EΩ),τd) is given in the case that E is a uniform algebra. As a consequence we get that in this case the algebra (HL(EΩ),τd) is semisimple.
- Subjects
ANALYTIC mappings; ALGEBRA; TOPOLOGICAL algebras; HOLOMORPHIC functions; TOPOLOGY; UNIFORM algebras; BANACH algebras; TOPOLOGICAL property
- Publication
Publications of the Research Institute for Mathematical Sciences, 2020, Vol 56, Issue 3, p431
- ISSN
0034-5318
- Publication type
Article
- DOI
10.4171/PRIMS/56-3-1