共查询到20条相似文献,搜索用时 31 毫秒
1.
Pervasive pre-Riesz spaces are defined by means of vector lattice covers. To avoid the computation of a vector lattice cover, we give two distinct intrinsic characterizations of pervasive pre-Riesz spaces. We introduce weakly pervasive pre-Riesz spaces and observe that this property can be easily checked in examples. We relate weakly pervasive pre-Riesz spaces to pre-Riesz spaces with the Riesz decomposition property. 相似文献
2.
BinodChandraTripathy SabitaMahanta 《应用数学学报(英文版)》2004,20(3):487-494
In this article we introduce the vector valued sequence space m(E_k,φ,∧),associated with themultiplier sequence ∧=(λ_k) of non-zero complex numbers,and the terms of the sequence are chosen from theseminormed spaces E_k,seminormed by f_k for all k∈N.This generalizes the sequence space m(φ) introducedand studied by Sargent.We study some of its properties like solidity,completeness,and obtain some inclusionresults.We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E_k,φ,∧).We prove some general results too. 相似文献
3.
4.
In a vector lattice, ideals and bands are well-investigated subjects. We study similar notions in a pre-Riesz space. The pre-Riesz
spaces are exactly the order dense linear subspaces of vector lattices. Restriction and extension properties of ideals, solvex
ideals and bands are investigated. Since every Archimedean directed partially ordered vector space is pre-Riesz, we establish
properties of ideals and bands in such spaces.
相似文献
5.
In this article we introduce the vector valued paranormed sequence spaces
and
defined over a seminormed space (X,q). We study their different properties like completeness, solidness, symmetry, convergence freeness etc. We prove some inclusion
results.
相似文献
6.
Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the usual star product of exponential type becomes continuous. Many properties of the resulting locally convex algebra are explained. We compare this approach to various other discussions of convergent star products in finite and infinite dimensions. We pay special attention to the case of a Hilbert space and to nuclear spaces. 相似文献
7.
8.
Onno van Gaans 《Indagationes Mathematicae》2003,14(1):15-30
As a generalization of the notion of Riesz seminorm, a class of seminorms on directed partially ordered vector spaces is introduced, such that (1) every seminorm in the class can be extended to a Riesz seminorm on every larger Riesz space that is majorized and (2) a seminorm on an order dense linear subspace of a Riesz space is in the class if and only if it can be extended to a Riesz seminorm on the Riesz space. The latter property yields that if a directed partially ordered vector space has an appropriate Riesz completion, then a seminorm on the space is in the class if and only if it is the restriction of a Riesz seminorm on the Riesz completion. An explicit formula for the extension is given. The class of seminorms is described by means of a notion of solid unit ball in partially ordered vector spaces. Some more properties concerning restriction and extension are studied, including extension to L- and M-seminorms. 相似文献
9.
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
10.
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.
11.
It will be shown that a normed partially ordered vector space is linearly, norm, and order isomorphic to a subspace of a normed Riesz space if and only if its positive cone is closed and its norm p satisfies p(x)p(y) for all x and y with -yxy. A similar characterization of the subspaces of M-normed Riesz spaces is given. With aid of the first characterization, Krein's lemma on directedness of norm dual spaces can be directly derived from the result for normed Riesz spaces. Further properties of the norms ensuing from the characterization theorem are investigated. Also a generalization of the notion of Riesz norm is studied as an analogue of the r-norm from the theory of spaces of operators. Both classes of norms are used to extend results on spaces of operators between normed Riesz spaces to a setting with partially ordered vector spaces. Finally, a partial characterization of the subspaces of Riesz spaces with Riesz seminorms is given. 相似文献
12.
M. Sioen 《Journal of Pure and Applied Algebra》2006,207(3):675
In this work we investigate the natural algebraic structure that arises on dual spaces in the context of quantified functional analysis. We show that the category of absolutely convex modules is obtained as the category of Eilenberg-Moore algebras induced by the dualization functor [−,R] on locally convex approach spaces. We also establish a dual adjunction between the latter category and the category of seminormed spaces. 相似文献
13.
S. Verwulgen 《Applied Categorical Structures》2006,14(2):111-121
Many structures in functional analysis are introduced as the limit of an inverse (aka projective) system of seminormed spaces [2, 3, 8]. In these situations, the dual is moreover equipped with a seminorm. Although the topology of the inverse limit is seldom metrizable, there is always a natural overlying locally convex approach structure. We provide a method for computing the adjoint of this space, by showing that the dual of a limit of locally convex approach spaces becomes a co-limit in the category of seminormed spaces. As an application we obtain an isometric representation of the dual space of real valued continuous functions on a locally compact Hausdorff space X, equipped with the compact open structure. 相似文献
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15.
M. M. Fel'dman 《Mathematical Notes》1975,18(6):1127-1133
We characterize the trace of a seminorm (norm) on a cone; we show that the linearly ordered set of seminorms with a given trace on a reproducing cone form a complete lattice. We obtain conditions for the existence of an adjoint seminorm and for the equivalence of norms with a given trace. 相似文献
16.
Egbert Dettweiler 《Monatshefte für Mathematik》1980,89(3):185-204
We study the problem under what conditions a cylindrical measure on a locally convex vector lattice is a Radon measure on the positive cone of the vector lattice. For some special vector lattices necessary and sufficient conditions are given. These results are applied to the construction of random measures on not necessarily locally compact state spaces. 相似文献
17.
Vladimir Dotsenko 《Selecta Mathematica, New Series》2009,14(2):229-245
We introduce several associative algebras and families of vector spaces associated to these algebras. Using lattice vertex
operators, we obtain dimension and character formulae for these spaces. In particular, we define a family of representations
of symmetric groups which turn out to be isomorphic to parking function modules. We also construct families of vector spaces
whose dimensions are Catalan numbers and Fuss–Catalan numbers respectively. Conjecturally, these spaces are related to spaces
of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras.
相似文献
18.
A.K. Katsaras 《Fuzzy Sets and Systems》1984,12(2):143-154
Some of the properties of the fuzzy seminormed and fuzzy normed spaces are studied. Also, the notion of a bornological fuzzy linear space is given and some of the properties of such a space are investigated. 相似文献
19.
《Quaestiones Mathematicae》2013,36(7):919-937
AbstractPre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover Y for a pre-Riesz space X, we address the question how to find vector lattice covers for subspaces of X, such as ideals and bands. We provide conditions such that for a directed ideal I in X its smallest extension ideal in Y is a vector lattice cover. We show a criterion for bands in X and their extension bands in Y as well. Moreover, we state properties of ideals and bands in X which are generated by sets, and of their extensions in Y. 相似文献
20.
A general Fatou Lemma is established for a sequence of Gelfand integrable functions from a vector Loeb space to the dual of a separable Banach space or, with a weaker assumption on the sequence, a Banach lattice. A corollary sharpens previous results in the finite-dimensional setting even for the case of scalar measures. Counterexamples are presented to show that the results obtained here are sharp in various aspects. Applications include systematic generalizations of the distribution of correspondences from the case of scalar Loeb spaces to the case of vector Loeb spaces and a proof of the existence of a pure strategy equilibrium in games with private and public information and with compact metric action spaces. 相似文献