A note on the left essential spectra of operator matrices

作者：Li, Yuan^*; Sun, Xiu Hong; Du, Hong Ke

来源：Acta Mathematica Sinica-English Series, 2007, 23(12): 2235-2240.

DOI：10.1007/s10114-007-0966-0

• left essential spectrum
• 2 x 2 operator matrix
• perturbations of spectra

When A epsilon B(H) and B epsilon B(K) are given, we denote by M-C the operator matrix acting on the infinite dimensional separable Hilbert space H circle plus K of the form M-C = ((A)(0) (C)(B)). In this paper, a necessary and sufficient condition for M-C to be left Fredholm for some C epsilon F(K, H) (C epsilon Inv (K, H)) is given, where F(K, H) and Inv(K, H) denote respectively, the set of Fredholm operators and the set of invertible operators of B(K, H). In addition, we give a necessary and sufficient condition for M-C to be left Fredholm for all C epsilon Inv (K, H).

• 出版日期2007-12
• 单位陕西师范大学