Perturbations of the right and left spectra for operator matrices. (English) Zbl 1261.47010
Summary: Let and be separable Hilbert spaces. For given and , denotes an operator acting on of the form , where and . In this paper, a necessary and sufficient condition is given for to be right invertible for some and . In addition, it is shown that, if dim , then is left invertible for some and ; if dim , then is left invertible for some and if and only if is closed and dim .
|47A10||Spectrum and resolvent of linear operators|
|47A55||Perturbation theory of linear operators|