scholarly journals Approximation Properties in Felbin Fuzzy Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 1003 ◽  
Author(s):  
Ju Myung Kim ◽  
Keun Young Lee
Keyword(s):  
Comparative Study ◽  
Finite Rank ◽  
Approximation Properties ◽  
Bounded Operators ◽  
Normed Spaces ◽  
New Concepts

In this paper, approximation properties in Felbin fuzzy normed spaces are considered. These approximation properties are new concepts in Felbin fuzzy normed spaces. Definitions and examples of such properties are given and we make a comparative study among approximation properties in Bag and Samanta fuzzy normed spaces and Felbin fuzzy normed spaces. We develop the representation of finite rank bounded operators in our context. By using this representation, characterizations of approximation properties are established in Felbin fuzzy normed spaces.

scholarly journals The evaluation functionals associated with an algebra of bounded operators

1969 ◽  
Vol 10 (1) ◽  
pp. 73-76 ◽  
Author(s):  
J. Duncan
Keyword(s):  
Banach Space ◽  
Normed Space ◽  
Finite Rank ◽  
Bounded Operators ◽  
Image Position

In this note we shall employ the notation of [1] without further mention. Thus X denotes a normed space and P the subset of X × X′ given byGiven a subalgebra of B(X), the set {Φ(X,f):(x,f) ∈ P} of evaluation functional on is denoted by II. We shall prove that if X is a Banach space and if contains all the bounded operators of finite rank, then Π is norm closed in ′. We give an example to show that Π need not be weak* closed in ″. We show also that FT need not be norm closed in ″ if X is not complete.

Approximation properties in fuzzy normed spaces

2016 ◽  
Vol 282 ◽  
pp. 115-130 ◽  
Author(s):  
Keun Young Lee
Keyword(s):  
Approximation Properties ◽  
Normed Spaces

scholarly journals Bounded approximation properties in terms of $C[0,1]$

2012 ◽  
Vol 110 (1) ◽  
pp. 45 ◽  
Author(s):  
Åsvald Lima ◽  
Vegard Lima ◽  
Eve Oja
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Approximation Property ◽  
Integral Operators ◽  
Operator Ideal ◽  
Approximation Properties ◽  
Finite Rank Operators ◽  
Nuclear Operators ◽  
The Ideal

Let $X$ be a Banach space and let $\mathcal I$ be the Banach operator ideal of integral operators. We prove that $X$ has the $\lambda$-bounded approximation property ($\lambda$-BAP) if and only if for every operator $T\in \mathcal I(X,C[0,1]^*)$ there exists a net $(S_\alpha)$ of finite-rank operators on $X$ such that $S_\alpha\to I_X$ pointwise and 26767 \limsup_\alpha\|TS_\alpha\|_{\mathcal I}\leq\lambda\|T\|_{\mathcal I}. 26767 We also prove that replacing $\mathcal I$ by the ideal $\mathcal N$ of nuclear operators yields a condition which is equivalent to the weak $\lambda$-BAP.

scholarly journals Invertible Operators on Soft Normed Spaces

2020 ◽  
pp. 1089-1097
Author(s):  
Sabah Aboud ◽  
Buthaina Abdul Hassan
Keyword(s):  
Linear Operator ◽  
Invertible Operator ◽  
Normed Spaces ◽  
Linear Spaces ◽  
New Concepts

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

Fuzzy logic and self-referential reasoning: a comparative study with some new concepts

2012 ◽  
Vol 41 (3) ◽  
pp. 331-357
Author(s):  
Mohammad Reza Rajati ◽  
Hamid Khaloozadeh ◽  
Witold Pedrycz
Keyword(s):  
Fuzzy Logic ◽  
Comparative Study ◽  
New Concepts

Generalized hybrid operators preserving exponential functions

2019 ◽  
Vol 12 (07) ◽  
pp. 1950089
Author(s):  
Deepika Agrawal ◽  
Vijay Gupta
Keyword(s):  
Asymptotic Formula ◽  
Comparative Study ◽  
Open Problem ◽  
Generating Functions ◽  
Graphical Representation ◽  
Type Theorem ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Convergence Estimate ◽  
Voronovskaya Type Theorem

The present paper deals with the approximation properties of generalization of Lupaş–Păltănea’s operators preserving exponential functions. We obtain moments using the concept of moment generating functions and establish a Voronovskaya type theorem, uniform convergence estimate and also an asymptotic formula in quantitative sense. In the end we present comparative study through graphical representation and propose an open problem.

Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts

1980 ◽  
Vol 23 (4) ◽  
pp. 401-411 ◽  
Author(s):  
H. Fakhoury
Keyword(s):  
Best Approximation ◽  
Compact Operators ◽  
Approximation Properties ◽  
Bounded Operators ◽  
Weakly Compact ◽  
The Best Approximation ◽  
Weakly Compact Operators

SommaireIt is shown that if V=C(X) or V = L1(μ) then the subspace of compact (resp. weakly compact) operators from V into itself is not an M-ideal in the space of bounded operators. This is the contrary to what happens when V= Co(ℕ) or lp(ℕ). The main result is proved via the best approximation properties of M-ideals and some results concerning norm one projections in C(X) and L1(μ) are deduced from this fact.

scholarly journals Quotient operators and the open mapping theorem

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6221-6227
Author(s):  
Mahesh Krishna ◽  
Sam Johnson
Keyword(s):  
Open Mapping ◽  
Bounded Operators ◽  
Normed Spaces ◽  
Open Mapping Theorem

Quotients of bounded operators on normed spaces have been discussed. Openmapping theorem for quotients of bounded operators and its consequences are given.

Spectral characterization of the socle in Jordan–Banach algebras

1995 ◽  
Vol 117 (3) ◽  
pp. 479-489 ◽  
Author(s):  
Bernard Aupetit
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Finite Rank ◽  
Banach Algebras ◽  
Spectral Characterization ◽  
Bounded Operators ◽  
Finite Rank Operators ◽  
Finite Dimensional ◽  
Minimal Idempotent

If A is a complex Banach algebra the socle, denoted by Soc A, is by definition the sum of all minimal left (resp. right) ideals of A. Equivalently the socle is the sum of all left ideals (resp. right ideals) of the form Ap (resp. pA) where p is a minimal idempotent, that is p2 = p and pAp = ℂp. If A is finite-dimensional then A coincides with its socle. If A = B(X), the algebra of bounded operators on a Banach space X, the socle of A consists of finite-rank operators. For more details about the socle see [1], pp. 78–87 and [3], pp. 110–113.

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