共查询到20条相似文献,搜索用时 15 毫秒
1.
Javier Alejandro Chávez-Domínguez 《Journal of Functional Analysis》2011,261(2):387-407
Building upon the ideas of R. Arens and J. Eells (1956) [1] we introduce the concept of spaces of Banach-space-valued molecules, whose duals can be naturally identified with spaces of operators between a metric space and a Banach space. On these spaces we define analogues of the tensor norms of Chevet (1969) [3] and Saphar (1970) [14], whose duals are spaces of Lipschitz p-summing operators. In particular, we identify the dual of the space of Lipschitz p-summing operators from a finite metric space to a Banach space — answering a question of J. Farmer and W.B. Johnson (2009) [6] — and use it to give a new characterization of the non-linear concept of Lipschitz p-summing operator between metric spaces in terms of linear operators between certain Banach spaces. More generally, we define analogues of the norms of J.T. Lapresté (1976) [11], whose duals are analogues of A. Pietsch?s (p,r,s)-summing operators (A. Pietsch, 1980 [12]). As a special case, we get a Lipschitz version of (q,p)-dominated operators. 相似文献
2.
Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π2(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π2(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open. 相似文献
3.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained. 相似文献
4.
S. Challal 《Journal of Mathematical Analysis and Applications》2009,355(2):700-707
We prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the p-Laplacian. 相似文献
5.
周泽华 《中国科学A辑(英文版)》2003,46(1):33-38
Let Un be the unit polydisc of Cn and φ= (φ1,...,φn? a holomorphic self-map of Un. Let 0≤α< 1. This paper shows that the composition operator Cφ, is bounded on the Lipschitz space Lipa(Un) if and only if there exists M > 0 such thatfor z∈Un. Moreover Cφ is compact on Lipa(Un) if and only if Cφ is bounded on Lipa(Un) and for every ε > 0, there exists a δ > 0 such that whenever dist(φ(z),σUn) <δ 相似文献
6.
We characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of ?p, Studia Math. 150 (2002) 17-33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summable operators. As application, the p-AP of dual Banach spaces is characterized via density of finite rank operators in the space of quasi-p-nuclear operators. This relates the p-AP to Saphar's approximation property APp′. As another application, the p-AP is characterized via a trace condition, allowing to define the trace functional on certain subspaces of the space of nuclear operators. 相似文献
7.
该文研究Lipschitz映射空间作为一个Banach空间的结构性质,主要研究了它的闭子空间有界线性算子空间(赋予算子范数)在其中的可余性. 相似文献
8.
Miroslav Pavlović 《Mathematische Zeitschrift》2008,258(1):81-86
We prove that maps into
if and only if belongs to . In the case β < 1, we give another two equivalent conditions.
Supported by MNZŽS Serbia, Project No. ON144010. 相似文献
9.
Kari Ylinen 《Proceedings of the American Mathematical Society》2005,133(5):1423-1425
In a recent paper Gutiérrez and Villanueva have used, without giving a detailed proof, an analogue of a well-known result of Ryan characterizing the weakly compact operators from a Banach space into the space of null sequences in a Banach space . In this note a counterexample is given showing that in the statement of Gutiérrez and Villanueva an additional condition is needed.
10.
We study the numerical radius of Lipschitz operators on Banach spaces via the Lipschitz numerical index, which is an analogue of the numerical index in Banach space theory. We give a characterization of the numerical radius and obtain a necessary and sufficient condition for Banach spaces to have Lipschitz numerical index 1. As an application, we show that real lush spaces and C -rich subspaces have Lipschitz numerical index 1. Moreover, using the Gâteaux differentiability of Lipschitz operators, we characterize the Lipschitz numerical index of separable Banach spaces with the RNP. Finally, we prove that the Lipschitz numerical index has the stability properties for the c0-, l1-, and l∞-sums of spaces and vector-valued function spaces. From this, we show that the C(K) spaces, L1(μ)-spaces and L∞(ν)-spaces have Lipschitz numerical index 1. 相似文献
11.
Lipschitz强增生算子方程逼近解的带误差的Ishikawa迭代程序 总被引:2,自引:0,他引:2
曾六川 《应用泛函分析学报》2002,4(3):274-279
设E是任意实Banach空间,T:E→E是Ligpschitz的强增生算子。证明了带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解。特别地,还给出了Ishikawa迭代序列的收敛率估计。另一方面,一个相关结果,讨论了E中Lipschitz强伪压缩映象的不动点的带误差的Ishikawa迭代序列的收敛性。 相似文献
12.
非线性Lipschitz算子的Lipschitz对偶算子及其应用 总被引:3,自引:0,他引:3
在文山中我们对非线性Lipschitz算子定义了其Lipschitz对偶算子,并证明了任意非线性Lipschitz算子的Lipschitz对偶算子是一个定义在Lipschitz对偶空间上的有界线性算子.本文还进一步证明:设C为 Banach空间 X的闭子集,C*L为C的 Lipschitz对偶空间,U为 C*L上的有界线性算子,则当且仅当 U为 w*-w*连续的同态变换时,存在Lipschitz连续算子T,使U为T的Lipschitz对偶算子.这一结论的理论意义在于:它表明一个非线性Lipschitz算子的可逆性问题可转化为有界线性算子的可逆性问题.作为应用,通过引入一个新概念──PX-对偶算子,在一般框架下给出了非线性算子半群的生成定理. 相似文献
13.
Lixin Cheng 《Journal of Mathematical Analysis and Applications》2010,371(2):407-413
Let X and Y be Banach spaces and T:Y→X be a bounded operator. In this note, we show first some operator versions of the dual relation between q-convexity and p-smoothness of Banach spaces case. Making use of them, we prove then the main result of this note that the two notions of uniform q-convexity and uniform p-smoothness of an operator T introduced by J. Wenzel are actually equivalent to that the corresponding T-modulus δT of convexity and the T-modulus ρT of smoothness introduced by G. Pisier are of power type q and of power type p, respectively. This is also an operator version of a combination of a Hoffman's theorem and a Figiel-Pisier's theorem. As their application, we show finally that a recent theorem of J. Borwein, A.J. Guirao, P. Hajek and J. Vanderwerff about q-convexity of Banach spaces is again valid for q-convexity of operators. 相似文献
14.
L. Thibault 《Journal of Optimization Theory and Applications》1985,46(2):205-213
It is proved that theV-subdifferential of a convex operator is locally Lipschitzian on the set of points at which it is continuous and subdifferentiable.Proposition 2.2 was originally stated for Holder continuity ofV-subdifferentials. The author would like to thank J. P. Penot for a very helpful suggestion which led to the present form of this proposition. 相似文献
15.
The Euclidean distortion of a metric space, a measure of how well the metric space can be embedded into a Hilbert space, is currently an active interdisciplinary research topic. We study the corresponding notion for mappings instead of spaces, which is that of Lipschitz factorization through subsets of Hilbert space. The main theorems are two characterizations of when a mapping admits such a factorization, both of them inspired by results dealing with linear factorizations through Hilbert space. The first is a nonlinear version of a classical theorem of Kwapień in terms of “dominated” sequences of vectors, whereas the second is a duality result by means of a tensor-product approach. 相似文献
16.
Banach空间的Lipschitz对偶及其应用 总被引:3,自引:0,他引:3
本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明:任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明:任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子.所获结果为推广线性算子理论到非线性情形(特别,运用线性算子理论研究非线性算子的特性)开辟了一条新的途径.作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理. 相似文献
17.
We construct examples which distinguish clearly the classes of p-hyponormal operators for 0<p?∞. In addition, we show that those examples classify the classes of w-hyponormal, absolute-p-paranormal, and normaloid operators on the complex Hilbert space. Only a few examples of p-hyponormal operators have been examined. Our technique can provide many examples related to the above operators. 相似文献
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In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the
Triebel-Lizorkin space. The operators include Littlewood-Paley operator and Marcinkiewicz operator. 相似文献