The Ascent and Descent of Semigroups of Operators
Lianping Zhang · Journal of Shanxi University · 2004
The ascent and descent of semigroups of linear operators are studied.The property that semigroups of operators with finite ascent and descent decompose the space into the direct sum was proved.The conditions under which ascent and descent of semigroups are finite have been presented.These properties are applied to some studies about eventuall normed continuous semigroup,and differentiable semigroup and completeness of root subspaces of an infinitesimal generator.