摘要
设Ｘ为Ｂａｎａｃｈ空间，Ω为复数域的开子集．文中给出了Ω上的拟预解Ｒ（·）（Ｂ（Ｘ））可由Ｘ上的一个多值线性算子Ａ定义的条件：ｘ∈Ｘ，存在｛λｎ｝Ω，使Ｗ－ｌｉｍｎ→∞Ｒ（λｎ）ｘ＝０；并证明了谱关系：复数λ∈σ（Ａ）当且仅当（μ－λ）－１∈σ（Ｒ（μ；Ａ））（λ≠μ）对多值算子及由其定义的拟预解也成立．
Let X be a Banach space and Ω be an unbounded open subset of C. The condition is given under which a pseudoresolvent R(·)(B(X)) on Ω can be defined by a multivalued linear operator A so that R(λ)=(λ-A)-1,λ∈Ω. That is :x∈X,{λn}Ω, so that λn→∞ and W-lim n→∞R(λn)x=0. Besides, It is proved that the spectral relationship: λ∈σ(A) if and only if (μ-λ)-1∈σ(R(μ;A)) for μ∈ρ(A) (λ≠μ), is also true for the multivalued linear operator A and the pseudoresolvent defined by A.
出处
《陕西师大学报（自然科学版）》
CAS
CSCD
北大核心
1998年第2期9-11,16,共4页
Journal of Shaanxi Normal University(Natural Science Edition)
基金
陕西省教委自然科学专项基金
关键词
多值线性算子
拟预解
谱
multivalued linear operator
pseudoresolvent
spectrum
