共查询到20条相似文献,搜索用时 0 毫秒
1.
Asghar Ranjbari Husain Saiflu 《Journal of Mathematical Analysis and Applications》2007,332(2):1097-1108
We define and study the projective and inductive limit notions for locally convex cones. We use convex quasiuniform structure method for this purpose. Also we study the barreledness in the locally convex cones and introduce the notion upper-barreled cones and prove that the inductive limit of upper-barreled cones is upper-barreled. 相似文献
2.
Vasile Postolica 《Journal of Global Optimization》1993,3(2):233-242
In this paper, the definition of supernormality for convex cones in locally convex spaces is discussed in detail on many interesting examples. Starting from the new direction for the study of the existence of efficient points (Pareto type optimums) in locally convex spaces offered by the concept of supernormal (nuclear) cone, we establish some existence results for the efficient points using boundedness and completeness of conical sections induced by non-empty subsets and we specify properties for the sets of efficient points beside important remarks 相似文献
3.
Walter Roth has investigated certain equivalence relations on locally convex cones in [W. Roth, Locally convex quotient cones, J. Convex Anal. 18, No. 4, 903–913 (2011)] which give rise to the definition of a locally convex quotient cone. In this paper, we investigate some special equivalence relations on a locally convex lattice cone by which the locally convex quotient cone becomes a lattice. In the case of a locally convex solid Riesz space, this reduces to the known concept of locally convex solid quotient Riesz space. We prove that the strict inductive limit of locally convex lattice cones is a locally convex lattice cone. We also study the concept of locally convex complete quotient lattice cones. 相似文献
4.
Walter Roth 《Proceedings of the American Mathematical Society》1998,126(7):1973-1982
We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.
5.
Marek Niezgoda 《Discrete Mathematics》2006,306(2):231-243
In this paper we give a systematic study of a class of linear inequalities related to convex cones in linear spaces. In particular, Chebyshev and Andersson type inequalities are discussed. Some classical and new inequalities are derived from the results. 相似文献
6.
In this paper, by developing the techniques of F. Dillen and L. Vrancken in [6], we study quasi-umbilical locally strongly convex homogeneous unimodular-affine hypersurfaces. We will present a characterization of a certain subclass in all dimensions; finally, in dimension five, we will give a complete classification of all quasi-umbilical homogeneous unimodular-affine hypersurfaces. 相似文献
7.
Let X be a real locally uniformly convex Banach space with normalized duality mapping J:X→2X*. The purpose of this note is to show that for every R>0 and every x0X there exists a function , which is nondecreasing and such that (r)>0 for r>0,(0)=0 and for all . Simply, it is shown that the necessity part of the proof of the original analogous necessary and sufficient condition of Prüß, for real uniformly convex Banach spaces, goes over equally well in the present setting. This is a natural setting for the study of many existence problems in accretive and monotone operator theories. 相似文献
8.
Lutz Dümbgen 《Annals of the Institute of Statistical Mathematics》1995,47(1):155-165
Let (P
: R
p
) be a simple shift family of distributions onR
p
, and letK R
p
be a convex cone. Within the class of nonrandomized tests ofK versusR
p
K, whose acceptance regionA satisfiesA=A+K, a test with minimal bias is constructed. This minimax test is compared to a likelihood ratio type test, which is optimal with respect to a different criterion. The minimax test is mimicked in the context of linear regression and one-sided tests for covariance matrices. 相似文献
9.
G. Y. Chen 《Journal of Optimization Theory and Applications》1995,84(1):93-101
This paper deals with generalizations of the Arrow-Barankin-Blackwell theorem in locally convex spaces, partially ordered by cones whose duals have nonempty quasi-interiors.This research has been partially supported by the World Laboratory, Lausanne, Switzerland, by the Department of Mathematics, University of Pisa, Pisa, Italy, and by the National Natural Sciences Foundation of China. Useful discussions with Professor F. Ferro are gratefully acknowledged. 相似文献
10.
Danes' Drop Theorem in locally convex spaces 总被引:11,自引:0,他引:11
Cheng Lixin Zhou Yunchi Zhang Fong 《Proceedings of the American Mathematical Society》1996,124(12):3699-3702
Danes' Drop Theorem is generalized to locally convex spaces.
11.
Mohammad Reza Motallebi 《Comptes Rendus Mathematique》2014,352(10):785-789
We investigate complete and compact subsets for the lower, upper and symmetric topologies of a locally convex cone and prove that weakly closed sets will be weakly compact, whenever they are weakly precompact. This leads to the weak* compactness of the polars of neighborhoods and weak compactness of the lower, upper and symmetric neighborhoods. 相似文献
12.
Walter Roth 《Transactions of the American Mathematical Society》1996,348(12):5065-5085
We introduce linear functionals on an ordered cone that are minimal with respect to a given subcone. Using concepts developed for Choquet theory we observe that the properties of these functionals resemble those of positive Radon measures on locally compact spaces. Other applications include monotone functionals on cones of convex sets, H-integrals on H-cones in abstract potential theory, and classical Choquet theory itself.
13.
14.
J. Ka?kol 《Journal of Mathematical Analysis and Applications》2007,332(2):965-974
Very recently Tkachuk has proved that for a completely regular Hausdorff space X the space Cp(X) of continuous real-valued functions on X with the pointwise topology is metrizable, complete and separable iff Cp(X) is Baire (i.e. of the second Baire category) and is covered by a family of compact sets such that Kα⊂Kβ if α?β. Our general result, which extends some results of De Wilde, Sunyach and Valdivia, states that a locally convex space E is separable metrizable and complete iff E is Baire and is covered by an ordered family of relatively countably compact sets. Consequently every Baire locally convex space which is quasi-Suslin is separable metrizable and complete. 相似文献
15.
A family of subsets of [n] is positive linear combination free if the characteristic vector of neither member is the positive linear combination of the characteristic vectors of some other ones. We construct a positive linear combination free family which contains (1-o(1))2n subsets of [n] and we give tight bounds on the o(1)2n term. The problem was posed by Ahlswede and Khachatrian [Cone dependence—a basic combinatorial concept, Preprint 00-117, Diskrete Strukturen in der Mathematik SFB 343, Universität Bielefeld, 2000] and the result has geometric consequences. 相似文献
16.
In this paper, we prove a general version of Ekeland's variational principle in locally convex spaces, where perturbations contain subadditive functions of topology generating seminorms and nonincreasing functions of the objective function. From this, we obtain a number of special versions of Ekeland's principle, which include all the known extensions of the principle in locally convex spaces. Moreover, we give a general criterion for judging the density of extremal points in the general Ekeland's principle, which extends and improves the related known results. 相似文献
17.
《Indagationes Mathematicae》2017,28(6):1157-1164
18.
Positivity - Using the coarsest weak topologies, we present the necessary and sufficient conditions for the weak upper, lower and symmetric compactness of subsets in cones. This leads us to... 相似文献
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20.
Asghar Ranjbari 《Positivity》2011,15(3):465-471
We propose a definition for strict inductive limits in locally convex cones. By this definition, we prove that the strict inductive limit of a sequence of locally convex cones with the strict separation property has the same strict separation property. Also we establish that the strict inductive limit of a sequences of separated cones is separated too. Finally we verify barreledness for this strict inductive limit. 相似文献