This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all po...Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.展开更多
文摘This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
基金supported by the NSF of Chinasupported by TRAPOYT and the NSF of China(No.10371046)
文摘Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.
