Perturbation Theory for Quasinilpotents in Banach Algebras

Xin Wang and Peng Cao
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Xin Wang: School of Artificial Intelligence, Jianghan University, Wuhan 430056, China
Peng Cao: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China

Mathematics, 2020, vol. 8, issue 7, 1-7

Abstract: In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then q n = 0 . Applications to C* algebras are given.

Keywords: perturbation theory; socle; quasinilpotent elements; finite spectrum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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