共查询到20条相似文献,搜索用时 125 毫秒
1.
Criteria for locally uniform convexity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz function spaces generated by locally uniformly convex Banach space, locally uniform convexity and strict convexity are equivalent. 相似文献
2.
吴奖伦 《应用数学学报(英文版)》1997,13(1):57-63
ThisworkissupportedinpartbythePostdoctoralScienceFoundationofChina.1.IntroductionTheclassicalBochnertheoremstatesthatafunctionCiR"-CisthecharacteristicfunctionofaprobabilitymeasureonR"iffCispositivedefinite,C(0)=1andcontinuous.FOrvariousgeneralizationsofthetheoremtoinfinitedimensionspaces,thereaderisreferredto{1]andT3I.Inthemonographl'],MinlostheoremgeneralizestheclassicalBochnertheoremtonuclearspaces,whichcharacterizestheclassofcharacteristicfunctionalsofRadonprobabilitymeasuresonstron… 相似文献
3.
Andreas H. Hamel 《Proceedings of the American Mathematical Society》2003,131(10):3025-3038
A generalization of Phelps' lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficiency theorem due to Isac. This solves a problem, concerning the drop theorem, proposed by G. Isac in 1997.
We show that a different formulation of Ekeland's principle in locally convex spaces, using a family of topology generating seminorms as perturbation functions rather than a single (in general discontinuous) Minkowski functional, turns out to be equivalent to the original version.
4.
Chi-Wing Wong 《Journal of Mathematical Analysis and Applications》2007,329(1):452-471
Daneš' drop theorem is extended to bornological vector spaces. An immediate application is to establish Ekeland-type variational principle and its equivalence, Caristi fixed point theorem, in bornological vector spaces. Meanwhile, since every locally convex space becomes a convex bornological vector space when equipped with the canonical von Neumann bornology, Qiu's generalization of Daneš' work to locally convex spaces is recovered. 相似文献
5.
We study the structure of bounded sets in the space L1{E} of absolutely integrable Lusin-measurable functions with values in a locally convex space E. The main idea is to extend the notion of property (B) of Pietsch, defined within the context of vector-valued sequences, to spaces of vector-valued functions. We prove that this extension, that at first sight looks more restrictive, coincides with the original property (B) for quasicomplete spaces. Then we show that when dealing with a locally convex space, property (B) provides the link to prove the equivalence between Radon–Nikodym property (the existence of a density function for certain vector measures) and the integral representation of continuous linear operators T: L1 → E, a fact well-known for Banach spaces. We also study the relationship between Radon–Nikodym property and the characterization of the dual of L1{E} as the space L∞{E′b}. 相似文献
6.
Ján Haluška 《Czechoslovak Mathematical Journal》1997,47(2):205-219
A generalization of I. Dobrakov's integral to complete bornological locally convex spaces is given. 相似文献
7.
8.
We present a natural way to cover an Archimedean directed ordered vector space E by Banach spaces and extend the notion of Bochner integrability to functions with values in E. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map. 相似文献
9.
In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property. 相似文献
10.
《Mathematische Nachrichten》2017,290(5-6):920-929
In this paper, we investigate the locally uniformly non‐square point of Orlicz–Bochner sequence spaces endowed with Luxemburg norm. Analysing and combining the generating function M and properties of the real Banach space X , we get sufficient and necessary conditions of locally uniformly non‐square point, which contributes to criteria for locally uniform non‐squareness in Orlicz–Bochner sequence spaces. The results generalize the corresponding results in the classical Orlicz sequence spaces. 相似文献
11.
Locally convex convolutor spaces are studied which consist of those distributions that define a continuous convolution operator mapping from the space of test functions into a given locally convex lattice of measures. The convolutor spaces are endowed with the topology of uniform convergence on bounded sets. Their locally convex structure is characterized via regularization and function-valued seminorms under mild structural assumptions on the space of measures. Many recent generalizations of classical distribution spaces turn out to be special cases of the general convolutor spaces introduced here. Recent topological characterizations of convolutor spaces via regularization are extended and improved. A valuable property of the convolutor spaces in applications is that convolution of distributions inherits continuity properties from those of bilinear convolution mappings between the locally convex lattices of measures. 相似文献
12.
Jun Kawabe 《Proceedings of the American Mathematical Society》2000,128(11):3291-3300
In this paper, we extend a type of Strassen's theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.
13.
Thomas E. Gilsdorf 《Mathematische Nachrichten》1992,159(1):139-147
We look for characterizations of those locally convex spaces that satisfy the strict Mackey convergence condition within the context of spaces with webs. We will say that a locally convex space has a boundedly compatible web if it has a web of absolutely convex sets whose members behave like zero neighborhoods in a metrizable locally convex space. It will be shown that these locally convex spaces satisfy the strict Mackey convergence condition. One consequence of this result will be a characterization of boundedly retractive inductive limits. We will also prove that if E is locally complete and webbed, then the strict Mackey convergence condition is equivalent to E having a boundedly compatible web. 相似文献
14.
Summary Some compactness results in the space of Bochner integrable functions in Banach spaces and in the space of integrably bounded multifunction with non empty convex weakly compact values are presented. Applications to minimization problems are given.
Pour terminer, nous remercions M.Valadier qui a lu attentivement ce papier. 相似文献
Pour terminer, nous remercions M.Valadier qui a lu attentivement ce papier. 相似文献
15.
16.
Defant [5] introduced the local Radon–Nikodym property for duals of locally convex spaces. This is a generalization of Asplund
spaces as defined in Banach space theory. In this paper we generalise Dunford"s Theorem [7] to Banach spaces with Schauder
decompositions and apply this result to spaces of holomorphic functions on balanced domains in a Banach space.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
Werner Ricker 《Monatshefte für Mathematik》1983,95(3):229-234
Using a vector version of the Bochner—Schoenberg test which characterizes the Fourier—Stieltjes transforms of measures, a criterion is presented, in terms of the resolvent map, which determines when a linear operator with real spectrum acting in a locally convex space is a scalar-type spectral operator. This is an extension of a recent result of S. Kantorovitz. 相似文献
18.
We introduce in this work some normed space notions such as norming, thin and thick sets in general locally convex spaces. We also study some effects of thick sets on the uniform boundedness-like principles in locally convex spaces such as “weak*-bounded sets are strong*-bounded if and only if the space is a Banach–Mackey space”. It is proved that these principles occur under some weaker conditions by means of thick sets. Further, we show that the thickness is a duality invariant, that is, all compatible topologies for some locally convex space have the same thick sets. 相似文献
19.
S L Yadava 《Proceedings Mathematical Sciences》1986,95(2):79-96
Ito’s stochastic integral is defined with respect to a Wiener process taking values in a locally convex space and Ito’s formula is proved. Existence and uniqueness theorem is proved in a locally convex space for a class of stochastic evolution equations with white noise as a stochastic forcing term. The stochastic forcing term is modelled by a locally convex space valued stochastic integral. 相似文献
20.
V. Montesinos 《manuscripta mathematica》1977,22(2):165-170
In this paper we prove a result similar to a generalization due to M. Valdivia (4) of a theorem of V.L. Klee (1), in the context of real locally convex spaces which possess a metrizable locally convex topology coarser than the Mackey topology. In particular, we obtain some criteria of reflexivity for metrizable locally convex spaces. A particular case works for complex spaces.We thank Prof. Valdivia for his help and constant orientation This work follows from his suggestions. 相似文献