Some simple proofs in holomorphic spectral theory
Volume 75 / 2007
Banach Center Publications 75 (2007), 9-15
MSC: Primary 46H40; Secondary 31A05, 46H10.
DOI: 10.4064/bc75-0-1
Abstract
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.
