Résumé:
Let X and Y two complex Banach spaces and (A;B) a pair of
bounded linear operators acting on X with value on Y: This paper is con-
cerned with spectral analysis of the pair (A;B): We establish some properties
concerning the spectrum of the linear operator pencils A B when B is not
necessarily invertible and 2 C: Also, we use the functional calculus for the
pair (A;B) to prove the corresponding spectral mapping theorem for (A;B):
In addition, we de ne the generalized Kato essential spectrum and the closed
range spectra of the pair (A;B) and we give some relationships between this
spectrums. As application, we describe a spectral analysis of quotient opera-
tors.
