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On unbounded perturbations of semigroups: Compactness and norm continuity
被引：0
作者：
Miao Li
Xiaohui Gu
Falun Huang
机构：
[1] Huazhong University of Science and Technology,Department of Mathematics
[2] Sichuan University,Department of Mathematics
来源：
Semigroup Forum
|
2002年
/
65卷
关键词：
Hilbert Space;
Banach Space;
Essential Spectrum;
Continuous Semigroup;
Transport Theory;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let A and B be the generators of strongly continuous semigroups (S(t))t ≥ 0 and (T(t))t ≥ 0, respectively. Denote by Δ (t) = T(t) − S(t). We show that if Δ(t) is norm continuous for t > 0 and R(λ,B) − R(λ,A) is compact for λ ∈ ρ(A)⋂ ρ(B) , then Δ(t) is compact. The converse is true if the perturbing operator is of Miyadera-Voigt-type. A characterization of norm continuity of Δ(t) in terms of the resolvents of the generators is given in Hilbert spaces.
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页码：58 / 70
页数：12
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