On a property of weak resolvents and its application to a spectral problem
Volume 66 / 1997
Annales Polonici Mathematici 66 (1997), 263-268
DOI: 10.4064/ap-66-1-263-268
Abstract
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
