Reza Saadati, Massoud Amini
In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of $D$-compactness and $D$-boundedness in probabilistic normed spaces.
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The idea of convex sets and various related results in 2-Probabilistic normed spaces were established in [HR]. In this paper, We obtain the concepts of convex series closedness, convex series compactness, boundedness and their interrelationships in Menger's 2-probabilistic normed space. Finally, the idea of $ \mathcal{D}- $ Boundedness in Menger's 2-probabilistic normed spaces and Menger's Generalized 2-Probabilistic Normed spaces are discussed.
The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension Theorem with the help of bounded b-linear functionals in the case of linear n-normed spaces and discuss some examples and applications. Finally, we present the concept of weak*convergence for the sequence of bounded b-linear functionals in linear n-normed space.
In this paper, we will see that the Cartesian product of two 2-Banach spaces is also 2-Banach space and discuss some properties of closed linear operator in linear 2-normed space. We also describe the concept of different types of continuity of b-linear functional and derive the Uniform Boundedness Principle and Hahn-Banach extension theorem for b-linear functionals in the case of linear 2-normed spaces. We also introduce the notion of weak*convergence for the sequence of bounded b-linear functionals relative to linear 2-normed space.
Bounded Multilinear Functionals and Multicontinuous Functions on n-Normed Spaces
本文研究了n-范数空间中k-线性函数与k-连续函数的有界性及对偶空间的等价性。
The motivation of this paper is a suggestion by Höle of comparing the notions of $\D$-boundedness and boundedness in Probabilistic Normed spaces (briefly PN spaces), with non necessarily continuous triangle functions. Such spaces are here called ``pre-PN spaces''. Some results on Šerstnev spaces due to B. Lafuerza, J. A. Rodriguez, and C. Sempi, are here extended to generalized Šerstnev spaces (these are pre-PN spaces satisfying a more general Šerstnev condition). We also prove some facts on PN spaces (with continuous triangle functions). First, a connection between fuzzy normed spaces defined…
We define the ($w^\ast$-) boundedness property and the ($w^\ast$-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called ($w^\ast$-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of two $w^\ast$-thick sets in $\Xastast$ and $\Yast$ is a $w^\ast$-thick subset in $L(X,Y)^\ast$ and obtain as a concequense that the set $w^\ast -exp\:B_{K(l_2)^\ast}$ is $w^\ast$-thick.
On automatic boundedness of some operators in ordered Banach spaces
本文研究了从有序巴拿赫空间到范数空间的序到弱连续算子的有界性，证明在温和条件下此类算子均为有界。
Introducing Statistical Operators: Boundedness, Continuity, and Compactness
本文针对统计收敛在算子理论中的研究空白，定义并研究赋范空间间算子的统计有界性、连续性与紧性，并建立其与经典算子概念的联系。
In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional analysis, i.e. the open mapping, closed graph, principle of uniform boundedness and Banach-Steinhaus theorem in PN-spaces.
Collective order boundedness of sets of operators between ordered vector spaces
本文证明了序向量空间间算子集合的集体序有界性定理，并探讨了其在交换算子半群中的若干应用。
The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can fall in some normed spaces by defining suitable norms. The results for the mappings on the metrizable spaces can be applied to the operators on the space of bounded linear functionals corresponding to the Dirac's delta function.
Dually cone-boundedness of a set and applications
本文提出双锥有界性概念，探讨其与现有文献的联系，并展示其在扩展重要结果和技巧中的应用。
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and …
We prove sufficient conditions for the boundedness and compactness of Toeplitz operators $T_a$ in weighted sup-normed Banach spaces $H_v^\infty$ of holomorphic functions defined on the open unit disc $\mathbb{D}$ of the complex plane; both the weights $v$ and symbols $a$ are assumed to be radial functions on $\mathbb{D}$. In an earlier work by the authors it was shown that there exists a bounded, harmonic (thus non-radial) symbol $a$ such that $T_a$ is not bounded in any space $H_v^\infty$ with an admissible weight $v$. Here, we show that a mild additional assumption on the logarithmic decay r…
Weighted symbol spaces, magnetic translations, and pseudodifferential operators
该研究聚焦J. Sjöstrand提出的微局部有限正则性赋范符号空间相关伪微分算子，证明其在调制空间的有界性与Weyl合成积的连续性。
Boundedness in $L_p$ spaces for the Hartley-Fourier convolutions operator and their applications
本文研究 Hartley-Fourier 卷积算子的 $L_p$ 有界性，建立 Young 型不等式和赋范环结构，并应用于 Fredholm 型积分方程与 Barbashin 方程的可解性分析。
On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging
本研究在鲍施克和董的基础上，通过允许扰动、考虑闭半空间与超平面混合及使用动态加权和等方式扩展其关于松弛投影无穷乘积有界性的结果，还讨论推广局限并建立赋范空间压缩映射无穷乘积相关定理。
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