On the decomposition of the Riesz operator and the expansion of the Riesz semigroup

doi:10.1007/s00020-002-1288-3

	On the decomposition of the Riesz operator and the expansion of the Riesz semigroup
	Xu, GQ ; Feng, DX
刊名	INTEGRAL EQUATIONS AND OPERATOR THEORY
	2005-08-01
卷号	52 期号:4 页码:581-594
关键词	Riesz operator Riesz semigroup
ISSN号	0378-620X
DOI	10.1007/s00020-002-1288-3
英文摘要	For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues sigma(T)\{0} = {lambda(i)\ i >= 1}, denote by E(lambda(i); T) the eigen-projection corresponding to an eigenvalue lambda(i). In this paper we will show that if the operator sequence {T-n = Sigma(k=1)(n) E(lambda(k); T)T \n >= 1} is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T-p and T-r: T = T-p+T-r, where T-p is the weak limit of T-n and T-r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t >= tau. As an application, we consider the solution of transport equation on a bounded convex body.
WOS研究方向	Mathematics
语种	英语
出版者	BIRKHAUSER VERLAG AG
WOS记录号	WOS:000231771200008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/1237]
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, GQ
作者单位	1.Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xu, GQ,Feng, DX. On the decomposition of the Riesz operator and the expansion of the Riesz semigroup[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY,2005,52(4):581-594.
APA	Xu, GQ,&Feng, DX.(2005).On the decomposition of the Riesz operator and the expansion of the Riesz semigroup.INTEGRAL EQUATIONS AND OPERATOR THEORY,52(4),581-594.
MLA	Xu, GQ,et al."On the decomposition of the Riesz operator and the expansion of the Riesz semigroup".INTEGRAL EQUATIONS AND OPERATOR THEORY 52.4(2005):581-594.