Rendiconti del Circolo Matematico di Palermo

, Volume 51, Issue 3, pp 495–502

On operators with closed analytic core

  • T. Len Miller
  • Vivien G. Miller
  • Michael M. Neumann
Article

DOI: 10.1007/BF02871857

Cite this article as:
Miller, T.L., Miller, V.G. & Neumann, M.M. Rend. Circ. Mat. Palermo (2002) 51: 495. doi:10.1007/BF02871857

Abstract

As shown by Mbekhta [9] and [10], the analytic core and the quasi-nilpotent part of an operator play a significant role in the local spectral and Fredholm theory of operators on Banach spaces. It is a basic fact that the analytic core is closed whenever 0 is an isolated point of the spectrum. In this note, we explore the extent to which the converse is true, based on the concept of support points. Our results are exemplified in the case of decomposable operators, Riesz operators, convolution operators, and semi-shifts.

2000 Mathematics Subject Classification

47A1147A1047B4047B06

Key words and phrases

Local spectral theorydecomposable operatorsRiesz operators

Copyright information

© Springer 2002

Authors and Affiliations

  • T. Len Miller
    • 1
  • Vivien G. Miller
    • 1
  • Michael M. Neumann
    • 1
  1. 1.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA