The essential point spectrum of a regular operator

  • Lee, Woo-Young (Department of Mathematics Education, Sung Kyun Kwan University) ;
  • Lee, Hong-Youl (Department of Mathematics Education, Sung Kyun Kwan University) ;
  • Han, Young-Min (Department of Mathematics Education, Sung Kyun Kwan University)
  • Published : 1992.08.01

Abstract

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

Keywords