共查询到20条相似文献,搜索用时 0 毫秒
1.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
2.
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
3.
Elke Wolf 《Numerical Functional Analysis & Optimization》2013,34(5-6):646-651
Let φ: 𝔻 → 𝔻 and ψ: 𝔻 → ? be analytic maps. They induce a weighted composition operator ψ C φ acting between weighted Bloch type spaces and weighted Banach spaces of holomorphic functions. Under some assumptions on the weights, we give a necessary as well as a sufficient condition when such an operator is bounded resp. compact. 相似文献
4.
在序Banach空间中,研究了一类集值混合单调映象,用不同方法证明了两个新的耦合不动点存在性定理,所做工作扩充了文[5]的研究成果. 相似文献
5.
We establish an approximation criterion for essential self-adjointness of Dirichlet operators with nonconstant diffusion part on certain Banach spaces. 相似文献
6.
We introduce an iterative sequence for finding the solution to 0∈T(v), where T
:
E⇉E
* is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal.
3:239–249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417–429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an
estimate of the convergence rate of the algorithm. An application to minimization problems is given.
This work was partially supported by the National Natural Sciences Grant 10671050 and the Heilongjiang Province Natural Sciences
Grant A200607. The authors thank the referees for useful comments improving the presentation and Professor K. Kohsaka for
pointing out Ref. 7. 相似文献
7.
In this paper, we investigate the strong convergence of an inexact proximal-point algorithm. It is known that the proximal-point
algorithm converges weakly to a solution of a maximal monotone operator, but fails to converge strongly. Solodov and Svaiter
(Math. Program. 87:189–202, 2000) introduced a new proximal-type algorithm to generate a strongly convergent sequence and established a convergence result
in Hilbert space. Subsequently, Kamimura and Takahashi (SIAM J. Optim. 13:938–945, 2003) extended the Solodov and Svaiter result to the setting of uniformly convex and uniformly smooth Banach space. On the other
hand, Rockafellar (SIAM J. Control Optim. 14:877–898, 1976) gave an inexact proximal-point algorithm which is more practical than the exact one. Our purpose is to extend the Kamimura
and Takahashi result to a new inexact proximal-type algorithm. Moreover, this result is applied to the problem of finding
the minimizer of a convex function on a uniformly convex and uniformly smooth Banach space.
L.C. Zeng’s research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, China and by the Dawn Program Foundation in Shanghai.
J.C. Yao’s research was partially supported by the National Science Council of the Republic of China. 相似文献
8.
通过引入本性严格奇异算子和投影严格奇异算子,讨论本性不可比的Banach空间,对M.Gonzalez提出的猜想作出部分的肯定回答,最后,利用空间的本性不可比构造了一类空间,其上的非本性算子类和严格余奇异算子类是不重合的。 相似文献
9.
10.
In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations. 相似文献
11.
In this paper we study to what extent some classical results concerning operators T, from a
-space to a Banach space, or from a Banach space to a L
1-space, can be precised, when the Banach spaces involved are ordered (by a normal cone in the first case, by a closed generating
proper convex cone in the second case) and when the operators T are positive. 相似文献
12.
应用H-空间中的Park极大元定理,在Banach空间中证明了多值非单调算子的相补问题的解的存在性定理. 相似文献
13.
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
14.
通过构造格林函数,借助Banach空间中不连续增算子的不动点定理,研究了一类Banach空间中二阶微分方程周期边值问题解的存在性. 相似文献
15.
A necessary and sufficient condition for an operator in a Banach ideal space to be a prediction operator is given. 相似文献
16.
In this paper, by employing the notion of generalized projection operators and the well-known Fan’s lemma, we establish some
existence results for the variational inequality problem and the quasivariational inequality problem in reflexive, strictly
convex, and smooth Banach spaces. We propose also an iterative method for approximate solutions of the variational inequality
problem and we establish some convergence results for this iterative method.
L. C. Zeng, His research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in
Higher Education Institutions of MOE, China and by the Dawn Program Foundation, Shanghai, China.
J. C. Yao, His research was partially supported by the National Science Council of the Republic of China 相似文献
17.
Let X be a partially ordered real Banach space, let a,b∈X with a≤b. Let φ be a bounded linear functional on X. We say that X satisfies the box-optimization property (or X is a BOP space) if the box-constrained linear program: max 〈φ,x〉, s.t. a≤x≤b, has an optimal solution for any φ,a and b. Such problems arise naturally in solving a class of problems known as interval linear programs. BOP spaces were introduced (in a different language) and systematically studied in the first author’s doctoral thesis. In this paper, we identify new classes of Banach spaces that are BOP spaces. We present also sufficient conditions under which answers are in the affirmative for the following questions:
相似文献
- (i)When is a closed subspace of a BOP space a BOP space?
- (ii)When is the range of a bounded linear map a BOP space?
- (iii)Is the quotient space of a BOP space a BOP space?
18.
An operator
mapping a separable reflexive Banach space X into the dual space X is called increasing if
as
. Necessary and sufficient conditions for the superposition operators to be increasing are obtained. The relationship between the increasing and coercive properties of monotone partial differential operators is studied. Additional conditions are imposed that imply the existence of a solution for the equation
with an increasing operator A. 相似文献
19.
AbstractIn this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods. 相似文献
20.
Giampietro Allasia 《Numerical Functional Analysis & Optimization》2013,34(3):237-254
A class of cardinal basis functions is proposed in order to achieve a generalization to Banach spaces of Hermite-Birkhoff interpolation on arbitrarily distributed data. First, a constructive characterization of the class of cardinal basis functions is given. Then, the interpolation problem is solved by using a suitable combination of such functions and Taylor-Fréchet expansions. The performance of the obtained interpolants is improved by applying a localizing scheme, and the corresponding approximation error is estimated. A noteworthy case in Hilbert spaces and a numerical test comparing the Hermite-Birkhoff and Lagrange interpolants complete the presentation. 相似文献