共查询到20条相似文献,搜索用时 31 毫秒
1.
Yan Hua ZHANG Xiao Hong CAO College of Mathematics Information Science Shaanxi Normal University Shaanxi P. R. China 《数学研究与评论》2011,(5)
In this note we define the property (ω′), a variant of Weyl’s theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property (ω′) holds by means of the variant of the essential approximate point spectrum σ1(·) and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property (ω′) is discussed. 相似文献
2.
In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators. 相似文献
3.
In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index.In addition,the stability of property(ω) for H(P) operators is considered. 相似文献
4.
Wei Juan SHI Xiao Hong CAO 《数学学报(英文版)》2014,30(5):797-804
A Hilbert space operator T is said to have property(ω1) if σa(T)\σaw(T) ? π00(T), where σa(T) and σaw(T) denote the approximate point spectrum and the Weyl essential approximate point spectrum of T respectively, and π00(T) = {λ∈ iso σ(T), 0 dim N(T- λI) ∞}. If σa(T)\σaw(T) = π00(T), we say T satisfies property(ω). In this note, we investigate the stability of the property(ω1) and the property(ω) under compact perturbations, and we characterize those operators for which the property(ω1) and the property(ω) are stable under compact perturbations. 相似文献
5.
By the new spectrum originated from the single-valued extension property, we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω) holds. Meanwhile, the relationship between hypercyclic property(or supercyclic property)and property(ω) is discussed. 相似文献
6.
We call T ∈ B(H) consistent in Fredholm and index (briefly a CFI operator) if for each B ∈ B(H),T B and BT are Fredholm together and the same index of B,or not Fredholm together.Using a new spectrum defined in view of the CFI operator,we give the equivalence of Weyl’s theorem and property (ω) for T and its conjugate operator T* .In addition,the property (ω) for operator matrices is considered. 相似文献
7.
Qiaoling XIN Lining JIANG 《Frontiers of Mathematics in China》2014,9(6):1411-1426
We give the necessary and sufficient condition for a bounded linear operator with property (ω) by means of the induced spectrum of topological uniform descent, and investigate the permanence of property (ω) under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators. 相似文献
8.
In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index.In addition,the stability of property(ω) for H(P) operators is considered. 相似文献
9.
In this note we study the property(ω1),a variant of Weyl's theorem by means of the single valued extension property,and establish for a bounded linear operator defined on a Banach space the necessary and sufficient condition for which property(ω1) holds.As a consequence of the main result,the stability of property(ω1) is discussed. 相似文献
10.
In this note we define the property (ω′), a variant of Weyl’s theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property (ω′) holds by means of the variant of the essential approximate point spectrum σ1(·) and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property (ω′) is discussed. 相似文献
11.
In this note we study the property (ω), a variant of Weyl's theorem introduced by Rakocevic, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property (ω) and approximate Weyl's theorem hold. As a consequence of the main result, we study the property (ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators. 相似文献
12.
We define and study the weak* drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak* drop property for dual norm in a Banach space and a characterization of the sub-differentialmapping x→эp(x) from S(X) into 2^S(X*) that is norm upper semi-continuous and norm compact-valued. 相似文献
13.
Dan LI 《数学学报(英文版)》2012,28(9):1845-1850
Extending the notion of property T of finite von Neumann algebras to general von Neumann algebras, we define and study in this paper property T** for (possibly non-unital) C* -algebras. We obtain several results of property T** parallel to those of property T for unital C* -algebras. Moreover, we show that a discrete group Γ has property T if and only if the group C* -algebra Cr* (Γ) (or equivalently, the reduced group C* -algebra Cr* (Γ)) has property T**. We also show that the compact operators K(l2 ) has property T** but c0 does not have property T**. 相似文献
14.
This paper discusses“geometric property (T)”. This is a property of metric spaces introduced in earlier works of the authors for its applications to K-theory. Geometric property (T) is a strong form of “expansion property”, in particular, for a sequence (Xn) of bounded degree finite graphs, it is strictly stronger than (Xn) being an expander in the sense that the Cheeger constants h(Xn) are bounded below. In this paper, the authors show that geometric property (T) is a coarse invariant, i.e., it depends only on the large-scale geometry of a metric space X. The authors also discuss how geometric property (T) interacts with amenability, property (T) for groups, and coarse geometric notions of a-T-menability. In particular, it is shown that property (T) for a residually finite group is characterised by geometric property (T) for its finite quotients. 相似文献
15.
Qing MENG 《Frontiers of Mathematics in China》2020,15(2):385-398
We introduce and study property T and strong property T for unital*-homomorphisms between two unital C^*-algebras.We also consider the relations between property T and invariant subspaces for some canonical unital^-representations.As a corollary,we show that when G is a discrete group,G is finite if and only if G is amenable and the inclusion map i:Cr^*(G)→B(l^2(G))has property T.We also give some new equivalent forms of property T for countable discrete groups and strong property T for unital C^*-algebras. 相似文献
16.
We call T C B(H) consistent in Fredholm and index (briefly a CFI operator) if for each B ∈ B(H), TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl's theorem and property (ω) for T and its conjugate operator T^*. In addition, the property (ω) for operator matrices is considered. 相似文献
17.
《数学研究与评论》1992,(3)
It is well known that(Weakly)normal structure,(weak)sum-property,LD property andG。property are the fundamental tools in fixed points theory of nonexpansive mappings.Let X be a Banach space。(x_n)_(n∈N)be a bounded sequence of X.If for any point Xbe1onging to the convex hull covx((x_n)_(n∈N))of(x_n)_(n∈N),there ho1ds 相似文献
18.
Shiliang ZHAO 《数学年刊B辑(英文版)》2018,39(6):1001-1016
Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by △ the Laplace-Beltrami operator and by ▽ the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ‖△ 1/2 f‖Lp(ω) ≤ C‖|▽f|‖Lp(ω), for some range of p determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established. 相似文献
19.
《数学物理学报(B辑英文版)》2016,(1)
In this paper, we investigate the factor properties and gap sequence of the Tribonacci sequence, the fixed point of the substitution σ(a, b, c) =(ab, ac, a). Let ωpbe the p-th occurrence of ω and Gp(ω) be the gap between ωpand ω_(p+1). We introduce a notion of kernel for each factor ω, and then give the decomposition of the factor ω with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper:for each factor ω, the gap sequence {Gp(ω)}p≥1is the Tribonacci sequence over the alphabet{G_1(ω), G_2(ω), G_4(ω)}, and the expressions of gaps are determined completely. As an application, for each factor ω and p ∈ N, we determine the position of ωp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors. 相似文献
20.
The WAε property and g-NUCε, g-NUC Banach spaces are introduced. We prove that the WAε property is equivalent to the WBS property and the g-NUCε (resp., g-NUC) spaces are equivalent to the NUCε (resp. , NUC) spaces possessing the BS property. So we obtain a characterization of the NUCε (resp, , NUC) spaces possessing the BS property. 相似文献