scholarly journals A characterization of incomplete sequences in vector spaces

2012 ◽  
Vol 119 (1) ◽  
pp. 33-41
Author(s):  
Hoi H. Nguyen ◽  
Van H. Vu
Keyword(s):  
Vector Spaces

Induced L-bornological vector spaces and L-Mackey convergence1

2021 ◽  
Vol 40 (1) ◽  
pp. 1277-1285
Author(s):  
Zhen-yu Jin ◽  
Cong-hua Yan
Keyword(s):  
Complete Lattice ◽  
Vector Spaces ◽  
Specific Description ◽  
Equivalent Characterization ◽  
Fuzzy Setting

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

scholarly journals The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View

2005 ◽  
Vol 12 (03) ◽  
pp. 207-229 ◽  
Author(s):  
Gen Kimura ◽  
Andrzej Kossakowski
Keyword(s):  
Vector Space ◽  
Quantum State ◽  
Point Of View ◽  
Vector Spaces ◽  
Bloch Vector ◽  
State Spaces ◽  
Spherical Coordinate ◽  
N Level ◽  
Dual Property

Bloch-vector spaces for N-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We present a characterization of the space by using the spectra of (orthogonal) generators of SU (N). As an application, we find a dual property of the space which provides an overall picture of the space. We also provide three classes of quantum-state representations based on actual measurements and discuss their state-spaces.

scholarly journals Order-Lipschitz mappings restricted with linear bounded mappings in normed vector spaces without normalities of involving cones via methods of upper and lower solutions

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6691-6698
Author(s):  
Shujun Jiang ◽  
Zhilong Li
Keyword(s):  
Fixed Point ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Vector Spaces ◽  
Normed Vector Space ◽  
Unique Existence ◽  
Lipschitz Mappings ◽  
Normed Vector

In this paper, without assuming the normalities of cones, we prove some new fixed point theorems of order-Lipschitz mappings restricted with linear bounded mappings in normed vector space in the framework of w-convergence via the method of upper and lower solutions. It is worth mentioning that the unique existence result of fixed points in this paper, presents a characterization of Picard-completeness of order-Lipschitz mappings.

scholarly journals Characterizations of collectively precompact and semi-precompact opterators on topological vector spaces

1979 ◽  
Vol 28 (2) ◽  
pp. 179-188 ◽  
Author(s):  
M. V. Deshpande ◽  
S. M. Padhye
Keyword(s):  
Subject Classification ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Totally Bounded ◽  
Primary 47 ◽  
Bounded Sets ◽  
Locally Convex ◽  
Convex Spaces

AbstractCharacterizations of collectively precompact and collectively semi-precompact sets of operators on topological vector spaces are obtained. These lead to the characterization of totally bounded sets of semi-precompact operators on locally convex spaces.1980 Mathematics subject classification (Amer. Math. Soc): primary 47 B 05, 47 D 15; secondary 46 A 05, 46 A 15.

scholarly journals Bornologiese pseudotopologiese vektorruimtes

1990 ◽  
Vol 9 (1) ◽  
pp. 15-18
Author(s):  
M. A. Muller
Keyword(s):  
Vector Space ◽  
Inductive Limit ◽  
Vector Spaces ◽  
Topological Spaces ◽  
Direct Sums ◽  
Paper Properties ◽  
Topological Vector Spaces ◽  
Quotient Spaces ◽  
Locally Convex

Homological spaces were defined by Hogbe-Nlend in 1971 and pseudo-topological spaces by Fischer in 1959. In this paper properties of bornological pseudo-topological vector spaces are investigated. A characterization of such spaces is obtained and it is shown that quotient spaces and direct sums o f boruological pseudo-topological vector spaces are bornological. Every bornological locally convex pseudo-topological vector space is shown to be the inductive limit in the category of pseudo-topological vector spaces of a family of locally convex topological vector spaces.

Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces

2015 ◽  
Vol 4 (2) ◽  
pp. 47-55 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Linear Space ◽  
Linear Operators ◽  
Vector Spaces ◽  
Closed Space ◽  
Normed Spaces ◽  
Topological Vector Spaces ◽  
Compact Spaces ◽  
Inverse Theorems ◽  
Fuzzy Vector

In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

Inner structure in real vector spaces

2020 ◽  
Vol 27 (3) ◽  
pp. 361-366 ◽  
Author(s):  
Francisco Javier García-Pacheco ◽  
Enrique Naranjo-Guerra
Keyword(s):  
Convex Sets ◽  
Vector Spaces ◽  
Internal Point ◽  
Real Vector ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Intrinsic Characterization ◽  
The One ◽  
Locally Convex

AbstractInternal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

scholarly journals On a Characterization of Finite-Dimensional Vector Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-3
Author(s):  
Marat V. Markin
Keyword(s):  
Linear Operators ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
The Right

We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

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