Abstract
For a complex Banach algebra E , let H L ( E ) be the space of the mappings from E into E that are analytic in the sense of Lorch. We will show that H L ( E ) is a closed subalgebra of H b ( E , E ) and we will give a description of its spectrum. As an application we will show that E is semi-simple if and only if H L ( E ) is semi-simple. We will also give descriptions of the spectra of other algebras of analytic mappings in the sense of Lorch. In particular we will study the spectrum of the Banach algebra H L ∞ ( int B E ) of the bounded mappings from int B E into E that are analytic in the sense of Lorch.
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