We give a simple complex-variable proof of an old result of Zemánek and Le Page on the radical of a Banach algebra. Incidentally, the argument also proves a recent result of Harris and Kadison.
This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.
This paper will give a brief survey of ideas related to 'elements of finite closed descent' in certain kinds of topological algebra.
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