共查询到20条相似文献,搜索用时 15 毫秒
1.
引入了由非紧距离空间(D,d)到一般Banach空间Y中的Lipschitz-α算子以及相应的算子空间Lα(D,Y)和lα(D,Y),证明了Lipschitz-α算子空间Lα(D,Y)与lα(D,Y)∩Lα(D,Y)关于范数‖T‖α,e=‖Te‖ Lα(T)是Banach空间,并讨论了(lαB(D,Y),‖·‖α,e)、(LαB(D,Y),‖·‖α,e)及(Lα(D,Y),‖·‖α,e)之间的关系. 相似文献
2.
Zhan Dong LIANG Wen Xia WANG Sheng Jia LI 《数学学报(英文版)》2006,22(2):577-582
We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition. 相似文献
3.
Wei Gang SU Huai Jie ZHONG 《数学学报(英文版)》2006,22(2):515-522
This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space:
(a) Every generalized Riesz operator has the generalized West decomposition;
(b) Every operator makes strong Stampfli theorem true; Every operator has Apostol's compact correction. 相似文献
4.
Veil B. SHAKHMUROV 《数学学报(英文版)》2006,22(5):1493-1508
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters. 相似文献
5.
Lipschitz-α算子的M-谱理论 总被引:6,自引:0,他引:6
本文运用一个选定的可逆Lip-α算子M作为尺度算子(称为谱尺度),引入两个Banach空间之间的非线性Lip-α算子的M-豫解集、M-谱集、M-谱半径、豫解集、谱集及谱半径,证明了它们的一列系重要性质,给出了M-谱的一个摄动定理,初步建立了Lip-α算子的M-谱理论,使得现有的谱理论成为其特例. 相似文献
6.
In this paper,the perturbations of the Moore–Penrose metric generalized inverses of linear operators in Banach spaces are described.The Moore–Penrose metric generalized inverse is homogeneous and nonlinear in general,and the proofs of our results are different from linear generalized inverses.By using the quasi-additivity of Moore–Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition,we show some error estimates of perturbations for the singlevalued Moore–Penrose metric generalized inverses of bounded linear operators.Furthermore,by means of the continuity of the metric projection operator and the quasi-additivity of Moore–Penrose metric generalized inverse,an expression for Moore–Penrose metric generalized inverse is given. 相似文献
7.
Jin Chuan HOU Xiu Ling ZHANG 《数学学报(英文版)》2006,22(1):179-186
Let X be an infinite-dimensional complex Banach space and denote by B(X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B(X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B(X) such that either Φ(T) = cATA^-1 + ψ(T)I for all T, or Φ(T) = cAT*A^-1 + ψ(T)I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero. 相似文献
8.
Yakov ALBER Jin Lu LI 《数学学报(英文版)》2007,23(6):1109-1120
In this paper we study the connection between the metric projection operator PK : B →K, where B is a reflexive Banach space with dual space B^* and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K : B → K and πK : B^* → K. We also present some results in non-reflexive Banach spaces. 相似文献
9.
Zhao Fang BAI Jin Chuan HOU 《数学学报(英文版)》2005,21(5):1167-1182
Let X be a (real or complex) Banach space with dimension greater than 2 and let B0(X) be the subspace of B(X) spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0(X) which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф(T) = cATA^-1 or Ф(T) = cAT'A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T' denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B(X) preserving spectral radius has a similar form to the above with |c| = 1. 相似文献
10.
Let B(H) be the algebra of all the bounded linear operators on a Hilbert space H.For A,P and Q in B(H),if there exists an operator X∈ B(H) such thatAP X QA=A,X QAP X=X,(QAP X)*=QAP X and(X QAP)*=X QAP,then X is said to be the Γ-inverse of A associated with P and Q,and denoted by AP,Q+.In this note,we present some necessary and su?cient conditions for which A+P,Qexists,and give an explicit representation of AP,Q+(if AP,Q+exists). 相似文献
11.
Min Zhu ZHANG Wen XU 《数学学报(英文版)》2007,23(11):1991-2002
The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball. 相似文献
12.
The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given. 相似文献
13.
Operator Matrix Forms of Positive Operators 总被引:2,自引:0,他引:2
If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2)of operators on Hibert spaces is given,we proved that the operator ~↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R(A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet. 相似文献
14.
证明了 :在自反 Banach空间$X$中 ,每个闭子空间 L,都存在 X到 L上的拟线性投影算子 SL.一般说来 ,SL 既非度量投影算子 ,又非线性算子 . 相似文献
15.
Compactness of Product Operators on the Bergman Space 总被引:2,自引:0,他引:2
Mao Fa WANG Pei De LIU 《数学学报(英文版)》2005,21(4):723-732
In this paper, we study the compactness of the product of a composition operator with another one's adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given. 相似文献
16.
The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces(or little α-Bloch spaces) to H^∞, but also gives some estimates for the norm of the weighted composition operator. 相似文献
17.
Hardy-Orlicz Spaces and Their Multiplication Operators 总被引:2,自引:0,他引:2
Qun LU Guang Fu CAO Li Fang LIU 《数学学报(英文版)》2005,21(3):593-598
In this paper some formulae on the relationship between Hardy and Hardy Orlicz spaces are presented, and multiplication operators on Hardy-Orlicz spaces are discussed. 相似文献
18.
In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces. 相似文献
19.
Lan Zhe LIU Shan Zhen LU 《数学学报(英文版)》2006,22(1):69-76
Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ(|α|= m), The continuity of the operator on some Hardy and Herz type Hardy is obtained. 相似文献
20.
《数学研究与评论》1986,(4)
In [1] L. Nirenberg stated the following problem: Suppose T is a continuous map H→H (H is a Hilbert space), which is expanding,i.e. and T(0)=0.Suppose T map a neighborhood of the origin onto a neighborhood of the origin. Does T maps H onto H? In [2] Kung-Ching Chang and Li Shujie answered positively the problem when T is differentiable. 相似文献