Some simple proofs in holomorphic spectral theory

Volume 75 / 2007

Graham R. Allan Banach Center Publications 75 (2007), 9-15 MSC: Primary 46H40; Secondary 31A05, 46H10. DOI: 10.4064/bc75-0-1


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.


  • Graham R. AllanDepartment of Pure Mathematics and Mathematical Statistics
    Centre for Mathematical Sciences
    University of Cambridge
    Wilberforce Road
    Cambridge CB3 0WB

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