The spectrum of the multiplication operator associated with a family of operators in a Banach space
R. Denk, M. Möller, and C. Tretter
Abstract. An operator family of densely defined closed linear operators and the multiplication operator associated with it are considered. The spectrum of this multiplication operator is expressed in terms of the spectra of the operators in the given family.
Oper. Theory Adv. Appl. 162 (2005), 103-116.
The paper is available here: pdf