Some spectral properties of a bundle of linear operators in Banach space

The spectral properties of a bunch $A-\lambda B$, $D(A)\subseteq D(B)$, of linear closed densely defined operators in Banach space are considered. Our main result is a theorem to the effect that the spectrum of the bunch can be expanded with respect to a pair of direct sums; the theorem generalizes the celebrated theorem of Riesz concerning the expansion of the spectrum of an operator.