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

The spectral properties of a bunchA–B, D(A)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.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 847–857, December, 1977.