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Jin-xuan Fang - One of the best experts on this subject based on the ideXlab platform.
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New definition of Locally Convex L-topological vector spaces
Fuzzy Sets and Systems, 2009Co-Authors: Hua-peng Zhang, Jin-xuan FangAbstract:In this paper, a new definition of Locally Convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of Locally Convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization of the new Locally Convex L-topological vector spaces is presented. Finally, as applications of this characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-fuzzy sets in Locally Convex L-topological vector spaces are studied.
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On Locally Convex I-topological vector spaces
Fuzzy Sets and Systems, 2006Co-Authors: Hui Zhang, Jin-xuan FangAbstract:Abstract In this paper, the relation between two definitions of Locally Convex I -topological vector spaces is studied. These two definitions are introduced by Katsaras [Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984) 143–154] and Wu and Li [Convexity and fuzzy topological vector spaces, Science Exploration (China) 4(1) (1984) 1–4], respectively. We prove that the Locally Convex I -topological vector space in the sense of Wu and Li is a special case of that in the sense of Katsaras. We introduce the notion of generalized fuzzy semi-norm and prove that every Locally Convex I -vector topology in the sense of Katsaras on X can be determined by a family of generalized fuzzy semi-norms on X .
Camillo Trapani - One of the best experts on this subject based on the ideXlab platform.
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Locally Convex Quasi C*-Algebras and Their Structure
Lecture Notes in Mathematics, 2020Co-Authors: Maria Fragoulopoulou, Camillo TrapaniAbstract:Throughout this chapter \({{\mathfrak A}}_{\scriptscriptstyle 0}[\| \cdot \|{ }_{\scriptscriptstyle 0}]\) denotes a unital C*-algebra and τ a Locally Convex topology on \({{\mathfrak A}}_{\scriptscriptstyle 0}\). Let \(\widetilde {{{\mathfrak A}}_{\scriptscriptstyle 0}}[\tau ]\) denote the completion of \({{\mathfrak A}}_{\scriptscriptstyle 0}\) with respect to the topology τ. Under certain conditions on τ, a subspace \({\mathfrak A}\) of \(\widetilde {{{\mathfrak A}}_{\scriptscriptstyle 0}}[\tau ]\), containing \({{\mathfrak A}}_{\scriptscriptstyle 0}\), will form (together with \({{\mathfrak A}}_{\scriptscriptstyle 0}\)) a Locally Convex quasi *-algebra \(({\mathfrak A}[\tau ],{{\mathfrak A}}_{\scriptscriptstyle 0})\), which is named Locally Convex quasi C*-algebra. Examples and basic properties of such algebras are presented. So, let \({{\mathfrak A}}_{\scriptscriptstyle 0}[\| \cdot \|{ }_{\scriptscriptstyle 0}]\) and τ be as before, with {pλ}λ ∈ Λ a defining family of seminorms for τ. Suppose that τ satisfies the properties: (T1) \({{\mathfrak A}}_{\scriptscriptstyle 0}[\tau ]\) is a Locally Convex *-algebra with separately continuous multiplication. (T2) τ ≼∥⋅∥0.
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Locally Convex Quasi *-Algebras
Lecture Notes in Mathematics, 2020Co-Authors: Maria Fragoulopoulou, Camillo TrapaniAbstract:This chapter is devoted to Locally Convex quasi *-algebras and Locally Convex quasi C*-algebras. Both these notions generalize what we have discussed in Chaps. 3 and 5. The advantage is, of course, that the range of applications becomes larger and larger; the drawback is that the theory becomes more involved.
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Locally Convex quasi $C^*$-normed algebras
arXiv: Mathematical Physics, 2012Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:If $\ca_0[|\cdot|_0]$ is a $\cs$-normed algebra and $\tau$ a Locally Convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[\tau]$ (completion of $\ca_0[\tau]$) is a Locally Convex quasi *-algebra over $\ca_0$, but it is not necessarily a Locally Convex quasi *-algebra over the $\cs$-algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a Locally Convex quasi $\cs$-normed algebra, aiming at the investigation of $\widetilde{\ca_0}[\tau]$; in particular, we study its structure, *-representation theory and functional calculus.
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Locally Convex quasi c normed algebras
arXiv: Mathematical Physics, 2012Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:If $\ca_0[|\cdot|_0]$ is a $\cs$-normed algebra and $\tau$ a Locally Convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[\tau]$ (completion of $\ca_0[\tau]$) is a Locally Convex quasi *-algebra over $\ca_0$, but it is not necessarily a Locally Convex quasi *-algebra over the $\cs$-algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a Locally Convex quasi $\cs$-normed algebra, aiming at the investigation of $\widetilde{\ca_0}[\tau]$; in particular, we study its structure, *-representation theory and functional calculus.
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Locally Convex Quasi *-Algebras of Operators
Complex Analysis and Operator Theory, 2011Co-Authors: Camillo TrapaniAbstract:This note is mainly concerned with Locally Convex quasi C*-normed *-algebras which arise as completions of C*-algebras of operators under certain topologies. Their importance is made clear by the representation theory of abstract Locally Convex quasi C*-normed *-algebras, investigated in previous papers and whose basic aspects are also overviewed here.
Asghar Ranjbari - One of the best experts on this subject based on the ideXlab platform.
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Bornological Completion of Locally Convex Cones
Communications in Mathematical Analysis, 2020Co-Authors: Davood Ayaseh, Asghar RanjbariAbstract:In this paper, firstly, we obtain some new results about bornological convergence in Locally Convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for Locally Convex cones. Also, we prove that the completion of a bornological Locally Convex cone is bornological. We illustrate the main result by an example.
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A note on barreledness in Locally Convex cones
arXiv: Functional Analysis, 2019Co-Authors: Amir Dastouri, Asghar RanjbariAbstract: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.
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Dual neighborhood systems and polars in Locally Convex cones
Hacettepe Journal of Mathematics and Statistics, 2018Co-Authors: Somayyeh Jafarizad, Asghar RanjbariAbstract:In this paper, we define dual (abstract) neighborhood systems for Locally Convex cones. Also we consider three types of different polars and study some relations of them with bounded sets in Locally Convex cones.
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Some structure theorems on Locally Convex cones of linear operators
Le Matematiche, 2017Co-Authors: Davood Ayaseh, Asghar RanjbariAbstract:In this paper we investigate the structure of C(P,Q) (the cone of all continuous linear operators from Locally Convex cone (P,U) into Locally Convex cone (Q,W) , when (P,U) or (Q,W) are inductive or projective limit Locally Convex cones. We consider some special Convex quasiuniform structures on C(P,Q) , and prove some structure theorems.
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Completion of Locally Convex cones
Filomat, 2017Co-Authors: Davood Ayaseh, Asghar RanjbariAbstract:We define the concept of completion for Locally Convex cones. We show that how a Locally Convex cone with $(SP)$ can be embedded as an upper dense subcone in an upper complete Locally Convex cone with $(SP)$. We prove that every upper complete Locally Convex cone with $(SP)$ is also symmetric complete.
Liu Guo-fen - One of the best experts on this subject based on the ideXlab platform.
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The width in Locally Convex space
Analysis in Theory and Applications, 2003Co-Authors: Song Wenhua, Liu Guo-fenAbstract:In this paper we extend the problems of width in normed space to that in Locally Convex space and some results are given.
Song Wenhua - One of the best experts on this subject based on the ideXlab platform.
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The width in Locally Convex space
Analysis in Theory and Applications, 2003Co-Authors: Song Wenhua, Liu Guo-fenAbstract:In this paper we extend the problems of width in normed space to that in Locally Convex space and some results are given.
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The approximation on Locally Convex spaces
Approximation Theory and Its Applications, 1994Co-Authors: Song WenhuaAbstract:In this paper, we give some properties of f-approximation, f-Chebyshev centers and f-farthest points in Locally Convex spaces.
