On level sets of norm of generalized resolvent of operators pencils
Marwa Mansouri, Аммар Хеллаф, Hamza Guebbaï · Ufimskii Matematicheskii Zhurnal · 2024
We prove that the generalized resolvent operator defined in a Hilbert space cannot remain constant on any open subset of the resolvent set. Under certain conditions we also prove the same result for a complex uniformly convex Banach space. These results extend the known ones.