Amir Dastouri, Asghar Ranjbari
Locally convex cones are generalization of locally convex spaces. The assertion, whether a barreled cone is an upper-barreled cone or not, was posed as a question in [A. Ranjbari, H. Saiflu, Projective and inductive limits in locally convex cones, J. Math. Anal. Appl. 332 (2) (2007) 1097-1108]. In this paper, we show that a barreled locally convex cone is not necessarily upper-barreled.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Barreled extended locally convex spaces and Uniform boundedness principle
本文利用最精细局部凸拓扑（flc 拓扑）分析桶型扩展局部凸空间，通过考察下半连续半范数揭示了其与关联最精细局部凸空间的桶型性关系，并在扩展设定下建立了一致有界性原理。
We give the method of construction of normal but not strongly normal positive cones in Banach space.
Equivalent conditions that make the normal cone maximal monotone are investigated in the general settings of locally convex spaces. Some consequences such as Bishop Phelps and sum representability results are presented in the last part.
Hyers-Ulam Type Stability of the Pexiderized Cauchy Functional Equation in Locally Convex Cones
本文在局部凸锥的三种拓扑框架下研究Pexiderized Cauchy函数方程的Hyers-Ulam型稳定性，并给出若干重要推论。
We define the finest order on inductive limits of ordered cones which makes the linear mappings monotone and gives rise to the definition of inductive limit topologies for cones. Using the polars of neighborhoods, we establish embeddings between direct sums, inductive limits and their duals. These lead us to investigate the weak topologies and the topologies of pointwise convergence in inductive limits.
Hyers-Ulam Stability of Quadratic Operators in Locally Convex Cones
本文在局部凸锥框架下研究二次泛函方程的Hyers-Ulam稳定性，提出新的稳定性定理，深化了对二次算子受扰动时行为的理解，并推进了局部凸锥中稳定性理论的发展。
Denting Points of Convex Sets and Weak Property ($π$) of Cones in Locally Convex Spaces
本文将赋范空间中凸集凹陷点和锥的弱性质（π）的刻画推广到局部凸空间，建立凹陷点与连续点及端点之间的新等价关系，并解决向量优化中与锥的几何性质相关的若干问题。
Let $(E,ξ)={\rm ind}(E_n, ξ_n)$ be an inductive limit of a sequence $(E_n, ξ_n)_{n\in N}$ of locally convex spaces and let every step $(E_n, ξ_n)$ be endowed with a partial order by a pointed convex (solid) cone $S_n$. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence $(S_n)_{n\in N}$ of ordering cones is non-confli…
Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, ϕ : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that p(f(x), f(y)) \leq_K ϕ(p(x, y)), for all x, y \in X. We shall show that there exists a scalar comparison function ψ : R+ \rightarrow R+ and a metric d_p(in usual sense) on X such that d_p(f(x), f(y)) \leq ψ(d_p(x, y)), for all x, y \in X. Our results extend the results of Du (2010) [Wei-Shih Du, A note on cone metric fixed point theory and its equivalence, Nonlinear…
The tensor product of two ordered vector spaces can be ordered in more than one way, just as the tensor product of normed spaces can be normed in multiple ways. Two natural orderings have received considerable attention in the past, namely the ones given by the projective and injective (or biprojective) cones. This paper aims to show that these two cones behave similarly to their normed counterparts, and furthermore extends the study of these two cones from the algebraic tensor product to completed locally convex tensor products. The main results in this paper are the following: (i) drawing pa…
Additive and multiplicative maps in norm on the positive cone of continuous function algebras
本文研究了在连续函数代数正锥中满足范数加法和乘法条件的映射，证明此类映射为由同胚诱导的复合算子。
We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous actions, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem for Banach spaces. When restricting to cones that are locally compact in the weak topology, we prove that the property holds for all distal actions, thus extending the general Ryll-Nardzewski theorem for all locally convex spaces. Returning to arbitrary actions, the proposed fixed-point property becomes a group property, considerably stronger than amenabili…
Phase-isometries between the positive cones of the Banach space of continuous real-valued functions
本文研究连续实值函数空间正锥间的满射相位等距，证明其必由底空间同胚诱导，并可扩张为全空间上的满射线性等距。
A Banach space is locally almost square if, for every $y$ in its unit sphere, there exists a sequence $(x_n)$ in its unit sphere such that $\lim\|y\pm x_n\|=1$. A Banach space is weakly almost square if, in addition, we require the sequence $(x_n)$ to be weakly null. It is known that these two properties are distinct, so we aim to investigate if local almost squareness implies a weaker version of the latter property by replacing the sequence with a net. In order to achieve this result, we restrict ourselves to Banach lattices and introduce a strengthening of local almost squareness by requirin…
The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the r…
A mixed lattice vector space is a partially ordered vector space with two partial orderings, generalizing the notion of a Riesz space. Whereas the algebraic theory of mixed lattice structures dates back to the 1970s, the topological theory of mixed lattice spaces remains largely unexplored. The purpose of this paper is to develop the basic topological theory of mixed lattice spaces. A vector topology is said to be compatible with the mixed lattice structure if the mixed lattice operations are continuous. We obtain a characterization of compatible mixed lattice topologies, which is similar to t…
Order Isomorphisms between Positive Cones of $C_0(X)$
研究局部紧 Hausdorff 空间上 $C_0(X)$ 正锥之间的正齐次序同构，证明其可表示为由同胚和权重函数诱导的加权复合算子，并唯一延拓为线性序同构。
Lagrange Multipliers in locally convex spaces
本文研究了Hausdorff局部凸空间中含无穷多约束的数学规划问题，提出一般拉格朗日乘子规则，用Gateaux可微性替代Fréchet可微性，并引入“容许集”替代闭凸锥以推广现有结果。
Analysis on the cone of discrete Radon measures
本文研究了局部紧波兰空间上离散 Radon 测度锥的分析，讨论了概率测度、相关测度与相关函数，引入了离散生灭梯度与 Dirichlet 形式，并探讨了满足二项式恒等式的多项式函数系统。
For the Lie algebra $\g$ of a connected infinite-dimensional Lie group~$G$, there is a natural duality between so-called semi-equicontinuous weak-*-closed convex Ad^*(G)-invariant subsets of the dual space $\g'$ and Ad(G)-invariant lower semicontinuous positively homogeneous convex functions on open convex cones in $\g$. In this survey, we discuss various aspects of this duality and some of its applications to a more systematic understanding of open invariant cones and convexity properties of coadjoint orbits. In particular, we show that root decompositions with respect to elliptic Cartan suba…
Let $C$ be a cone in a locally convex Hausdorff topological vector space $X$ containing $0$. We show that there exists a (essentially unique) nonempty family $\mathscr{K}$ of nonempty subsets of the topological dual $X^\prime$ such that $$ C=\{x \in X: \forall K \in \mathscr{K}, \exists f \in K, \,\, f(x) \ge 0\}. $$ Then, we identify the additional properties on the family $\mathscr{K}$ which characterize, among others, closed convex cones, open convex cones, closed cones, and convex cones. For instance, if $X$ is a Banach space, then $C$ is a closed cone if and only if the family $\mathscr{K…
Let $g$ be a finite dimensional real Lie algebra. Let $r:g\to End(V)$ be a representation of $g$ in a finite dimensional real vector space. Let $C_{V}=(End(V)\tens S(g))^{g}$ be the algebra of $End(V)$-valued invariant differential operators with constant coefficients on $g$. Let $U$ be an open subset of $g$. We consider the problem of determining the space of generalized functions $ϕ$ on $U$ with values in $V$ which are locally invariant and such that $C_{V}ϕ$ is finite dimensional. In this article we consider the case $g=sl(2,R)$. Let $N$ be the nilpotent cone of $sl(2,R)$. We prove that whe…
Let $S$ be a closed subset of a Banach space $X$. Assuming that $S$ is epi-Lipschitzian at $\bar{x}$ in the boundary $ \bd S$ of $S$, we show that $S$ is strictly Hadamard differentiable at $\bar{x}$ IFF the Clarke tangent cone $T(S, \bar{x})$ to $S$ at $\bar{x}$ contains a closed hyperplane IFF the Clarke tangent cone $T(\bd S, \bar{x})$ to $\bd S$ at $\bar{x}$ is a closed hyperplane. Moreover when $X$ is of finite dimension, $Y$ is a Banach space and $g: X \mapsto Y$ is a locally Lipschitz mapping around $\bar{x}$, we show that $g$ is strictly Hadamard differentiable at $\bar{x}$ IFF $T(\mat…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。