Hilbert空阎上Lyapunov定理及其推广

THE LYAPUNOV THEOREM IN HILBERT SPACE AND ITS GENERALIZATION

研究Ｈｉｌｂｅｒｔ空间上Ｌｙａｐｕｎｏｖ定理．给出了Ｈｉｌｂｅｒｔ空间上有界线性算子的谱包含在右（左）半开平面内的充要条件，并将Ｌｙａｐｕｎｏｖ定理推广到一般形式．

in this paper, the Lyapunov theorem of a bounded linear operator in Hilbertspace is discussed. The necessary and sufficient conditions are given to determine that the spectrum of the bounded linear operator is included in the right (or left) plane. Finally, the Lyapunovtheorem is generalized.