2019/12/01 by Miloš Cvetković, Cvetković, Miloš D., Snežana Č. Živković-Zlatanović +1
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces
paper · pdf · doi:10.48550/arxiv.1912.00435
Let T be a bounded linear operator on a Banach space X. We give new necessary and sufficient conditions for T to be Drazin or Koliha-Drazin invertible. All those conditions have the following form: T possesses certain decomposition property and zero is not an interior point of some part of the spectrum of T. In addition, we study operators T satisfying Browder\textquoteright s theorem, or a-Browder\textquoteright s theorem, by means of some relationships between diferent parts of the spectrum of T.