摘要
在局部凸空间中引入了Ｙｏｓｉｄａ算子的概念，讨论了它的一些性质，得到：定理２设Ｘ是局部凸空间，则Ｘ上的每个全有界算子是Ｙｏｓｉｄａ子．定理５设Ｔ是局部凸空间Ｘ上的全有界算子，若对某个复数λ，算子Ｒλ＝（λＩ一Ｔ）－１存在且为Ｘ上的连续线性算子，则Ｒλ为Ｙｏｓｉｄａ算子．定理６设Ｘ是序列完备的局部凸空间，Ｔ是Ｘ上的Ｙｏｓｉｄａ算子，则由级数（｜λ｜＞β（Ｔ））所定义的算子Ｒ（λ）是Ｙｏｓｉｄａ算子．
The concept of Yosida operators is introduced in locally convex spaces. Some properties of it arediscussing.The main results are these.Theorem 2 Let X be a locally convex space,then every total bounded operator on X is a Yosidaoperator.Theorem 5 Suppose T is a total bounded operator on locally convex space X, let λ be a complexnumber,operator Rλ=(λf-T)-1 be continuous on X, then Rλis a Yosida operator.Theorem 6 Let X be a sequentially complete locally convex space,T be a Yosida operator onX. Then R(λ)which is defined by is a Yosida operator.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1996年第2期109-114,共6页
Journal of Southwest China Normal University(Natural Science Edition)
