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J. Haberl 《Journal of Optimization Theory and Applications》2004,121(2):327-359
The major part of the investigation is related to the problem of maximizing an upper semicontinuous quasiconvex functional f over a compact (possibly nonconvex) subset K of a real Hausdorff locally convex space E. A theorem by Bereanu (Ref. 1) says that the condition f is quasiconvex (quasiconcave) on K is sufficient for the existence of maximum (minimum) point of f over K among the extreme points of K. But, as we prove by a counterexample, this is not true in general. On the further condition that the convex hull of the set of extreme points of K is closed, we show that it is sufficient to claim that f is induced-quasiconvex on K to achieve an equivalent conclusion. This new concept of quasiconvexity, which we define by requiring that each lower-level set of f can be represented as the intersection of K with some convex set, is suitable for functionals with a nonconvex domain. Under essentially the same conditions, we prove that an induced-quasiconvex functional f is directionally monotone in the sense that, for each y K, the functional f is increasing along a line segment starting at y and running to some extreme point of K. In order to guarantee the existence of maximum points on the relative boundary r K of K, it suffices to make weaker demands on the function f and the space E. By introducing a weaker kind of directional monotonicity, we are able to obtain the following result: If f is i.s.d.-increasing i.e., for each y y K, there is a half-line emanating from y such that f is increasing along this half-line, then f attains its maximum at rK , even if E is a topological linear Hausdorff space (infinite-dimensional and not necessarily locally convex). We state further a practical method of proving i.s.d.-monotonicity for functions in finite-dimensional spaces and we discuss also some aspects of classification. 相似文献
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Let(E,γ)bealocallyconvexspaceandE′itsconjugatespace.AE′beanequicontinu-ousseton(E,γ).ThewellknownAlaoglu-BourbakiTheorem([1]P248)statesthateache-quicontinuousseton(E,γ)isσ(E′,E)relativelycompactsubset.Nevertheless,equicontinuoussetisσ(E′,E)relativel… 相似文献
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C. Blondia 《Mathematische Nachrichten》1983,114(1):335-341
Reflexive BANCH spaces and separable duals of BANACH spaces posses the RADON -NIKODYM Property. The purpose of this paper is to extend these results to locally convex spaces. As the examples will show, these RNP-spaces include most spaces which occur frequently in Functional Analysis. 相似文献
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证明了局部凸空间中非凸集上的上半连续凝集值映射的一个Leray-Schauder型不动点定理,并推广了一些已知的不动点定理。 相似文献
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利用广义模糊半范数族来研究了Katsaras意义下的局部凸Ⅰ-拓扑线性空间的某些性质,如分离性、模糊点网的收敛性、模糊集的有界性,以及同一个集上两个局部凸Ⅰ-拓扑的“粗“细”比较等。 相似文献
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P. R. Fuchs 《Results in Mathematics》1996,30(1-2):45-54
We consider the near-ring C(V) of all continuous operators on a locally convex space V. Like in the Theorem of Stone-Weierstrass the question arises which subnear-rings N have the property that every operator in C(V) can be approximated by elements of N on compact subsets of V. It is our aim to show that this can be achieved with certain primitive subnear-rings of C(V). For this we invoke a deep Theorem of Wielandt-Betsch on interpolation properties of primitive near-rings. We also stress the fact that such a Theorem of Stone-Weierstrass type can only be obtained in the context of near-rings. 相似文献
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Proper Efficiency in Locally Convex Topological Vector Spaces 总被引:18,自引:0,他引:18
We present a general treatment of proper efficiency, which was originally given in normed vector spaces; we introduce a new kind of efficiency in locally convex topological vector spaces. We examine the relationships among these efficiencies. As an application, we prove a strong Ekeland variational principle. 相似文献
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Klaus Jürgen Lorenz 《Mathematische Nachrichten》1986,129(1):91-101
The notion of strict differentiability in BANACH spaces is generalized to locally convex spaces in such a way, that computations in the bornological operator ideal of bounded operators play the role of norm estimations. We get a remarkably rich theory including not only the easy formulas like the chain rule, but also the deep theorems like the implicit function theorem. The BANACH space proofs can be translated almost literally. 相似文献
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Weakly Unconditional Cauchy Series on Locally Convex SpacesLiRonglu(李容录)(DepartmentofMathematics,HarbinInstituteofTechnology,... 相似文献
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Transitive and Hypercyclic Operators on Locally Convex Spaces 总被引:2,自引:0,他引:2
Bonet J.; Frerick L.; Peris A.; Wengenroth J. 《Bulletin London Mathematical Society》2005,37(2):254-264
Solutions are provided to several questions concerning topologicallytransitive and hypercyclic continuous linear operators on Hausdorfflocally convex spaces that are not Fréchet spaces. Amongothers, the following results are presented. (1) There existtransitive operators on the space of all finite sequences endowedwith the finest locally convex topology (it was already knownthat there is no hypercyclic operator on . (2) The space ofall test functions for distributions, which is also a completedirect sum of Fréchet spaces, admits hypercyclic operators.(3) Every separable infinite-dimensional Fréchet spacecontains a dense hyperplane that admits no transitive operator.2000 Mathematics Subject Classification 47A16 (primary), 46A03,46A04, 46A13, 37D45 (secondary). 相似文献
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提出了一类带有参数的向量值积分的优化问题,将H ardy空间中的一些概念推广到了局部凸空部间,尤其是将H ankel算子、最小模型匹配误差、最优解等概念推广到了局部凸空间. 相似文献
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A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 总被引:1,自引:0,他引:1
This paper presents a geometric characterization of convex sets in locally convex spaces on which a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem of w Asplund spaces a localized setting. 相似文献
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Let E be a complete, barrelled locally convex space, let V = (vn) be an increasing sequence of strictly positive, radial, continuous, bounded weights on the unit disc 𝔻 of the complex plane, and let φ be an analytic self map on 𝔻. The composition operators Cφ : f → f ○ φ on the weighted space of holomorphic functions HV (𝔻, E) which map bounded sets into relatively weakly compact subsets are characterized. Our approach requires a study of wedge operators between spaces of continuous linear maps between locally convex spaces which extends results of Saksman and Tylli [31, 32], and a representation of the space HV (𝔻, E) as a space of operators which complements work by Bierstedt , Bonet and Galbis [4] and by Bierstedt and Holtmanns [6]. 相似文献