Linear Operators on Normed Spaces

2020 ◽  
pp. 115-152
Author(s):  
James K. Peterson
Keyword(s):  
Linear Operators ◽  
Normed Spaces

scholarly journals Bidual Spaces and Reflexivity of Real Normed Spaces

2014 ◽  
Vol 22 (4) ◽  
pp. 303-311
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Real Number ◽  
Normed Space ◽  
Uniform Boundedness ◽  
Linear Operators ◽  
Linear Functionals ◽  
Normed Spaces ◽  
Boundedness Theorem ◽  
Natural Mapping ◽  
Real Normed Space ◽  
Banach Theorem

Summary In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals as linear operators by this definition. Accordingly we proved Uniform Boundedness Theorem for linear functionals using the theorem (5) from [21]. Finally, we defined reflexivity of real normed spaces and proved some theorems about isomorphism of linear operators. Using them, we proved some properties about reflexivity. These formalizations are based on [19], [20], [8] and [1].

scholarly journals Quantities related to upper and lower semi-Fredholm type linear relations

2002 ◽  
Vol 66 (2) ◽  
pp. 275-289 ◽  
Author(s):  
Teresa Alvarez ◽  
Ronald Cross ◽  
Diane Wilcox
Keyword(s):  
Perturbation Theory ◽  
General Setting ◽  
Linear Operators ◽  
Normed Spaces ◽  
Fredholm Type ◽  
Linear Relations ◽  
Lower Semi ◽  
Strictly Singular

Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F− linear relations. Applications to perturbation theory follow.

scholarly journals Exponential numbers of linear operators in normed spaces

1995 ◽  
Vol 219 ◽  
pp. 225-260 ◽  
Author(s):  
P. Enflo ◽  
V.I. Gurarii ◽  
V. Lomonsov ◽  
Yu.I. Lyubich
Keyword(s):  
Linear Operators ◽  
Normed 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.

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