scholarly journals Some generalizations of ascent and descent for linear operators

2021 ◽  
Author(s):  
Zied Garbouj
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Positive Operator ◽  
Finite Rank ◽  
Operator Theory ◽  
Compact Operators ◽  
Linear Operators ◽  
Linear Spaces ◽  
Basic Properties ◽  
Stability Results

AbstractThe purpose of this paper is to present in linear spaces some results for new notions called A-left (resp., A-right) ascent and A-left (resp., A-right) descent of linear operators (where A is a given operator) which generalize two important notions in operator theory: ascent and descent. Moreover, if A is a positive operator, we obtain several properties of ascent and descent of an operator in semi-Hilbertian spaces. Some basic properties and many results related to the ascent and descent for a linear operator on a linear space Kaashoek (Math Ann 172:105–115, 1967), Taylor (Math Ann 163:18–49, 1966) are extended to these notions. Some stability results under perturbations by compact operators and operators having some finite rank power are also given for these notions.

scholarly journals Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1643
Author(s):  
S. Chatterjee ◽  
T. Bag ◽  
Jeong-Gon Lee
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Present Article ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Compact Operators ◽  
Linear Spaces ◽  
Basic Properties ◽  
Fuzzy Setting

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo’s generalization of the Schauder-type fixed point theorem is developed for the class of ψ-set contractions. This theorem is proven by using the idea of the measure of non-compactness.

Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness

2020 ◽  
Vol 16 (01) ◽  
pp. 177-193
Author(s):  
Mami Sharma ◽  
Debajit Hazarika
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Compact Operators ◽  
Linear Operators ◽  
Bounded Linear ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
The Relationship

In this paper, we first investigate the relationship between various notions of fuzzy boundedness of linear operators in fuzzy normed linear spaces. We also discuss the fuzzy boundedness of fuzzy compact operators. Furthermore, the spaces of fuzzy compact operators have been studied.

scholarly journals Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces

2019 ◽  
Vol 16 (1) ◽  
pp. 0104
Author(s):  
Kider Et al.
Keyword(s):  
Compact Operator ◽  
Normed Space ◽  
Bounded Operator ◽  
Convergent Subsequence ◽  
Compact Operators ◽  
Bounded Sequence ◽  
Linear Operators ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Definition Of

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.

A separable quasidiagonal C*-algebra with a non-quasidiagonal quotient by the compact operators

1991 ◽  
Vol 110 (1) ◽  
pp. 143-145 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Finite Rank ◽  
Separable Hilbert Space ◽  
Compact Operators ◽  
C Algebra ◽  
Alternative Characterization ◽  
Image Position ◽  
Algebra Of Operators

A C*-algebra A of operators on a separable Hilbert space H is said to be quasidiagonal if there is an increasing sequence E1, E2, … of finite-rank projections on H tending strongly to the identity and such thatas i → ∞ for T∈A. More generally a C*-algebra is quasidiagonal if there is a faithful *-representation π of A on a separable Hilbert space H such that π(A) is a quasidiagonal algebra of operators. When this is the case, there is a decomposition H = H1 ⊕ H2 ⊕ … where dim Hi < ∞ (i = 1, 2,…) such that each T∈π(A) can be written T = D + K where D= D1 ⊕ D2 ⊕ …, with Di∈L(Hi) (i = 1, 2,…), and K is a compact linear operator on H. As is well known (and readily seen), this is an alternative characterization of quasidiagonality.

scholarly journals Properties (S) and (gS) for bounded linear operators

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1641-1652 ◽  
Author(s):  
M.H.M. Rashid
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Finite Rank ◽  
Linear Operators ◽  
Finite Multiplicity ◽  
Bounded Linear ◽  
Weyl Type Theorems ◽  
Weyl Theorem ◽  
Polaroid Operator ◽  
Isolated Eigenvalues

An operator T acting on a Banach space X obeys property (R) if ?0a(T) = E0(T), where ?0a(T) is the set of all left poles of T of finite rank and E0(T) is the set of all isolated eigenvalues of T of finite multiplicity. In this paper we introduce and study two new properties (S) and (gS) in connection with Weyl type theorems. Among other things, we prove that if T is a bounded linear operator acting on a Banach space, then T satisfies property (R) if and only if T satisfies property (S) and ?0(T) = ?0a(T), where ?0(T) is the set of poles of finite rank. Also we show if T satisfies Weyl theorem, then T satisfies property (S). Analogous results for property (gS) are given. Moreover, these properties are also studied in the frame of polaroid operator.

scholarly journals ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

2021 ◽  
pp. 595
Author(s):  
Chiranjib Choudhury ◽  
Shyamal Debnath
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Cauchy Sequences ◽  
Convergence Of Sequences

In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.

A Class of Positive Linear Operators

1968 ◽  
Vol 11 (1) ◽  
pp. 51-59 ◽  
Author(s):  
J. P. King
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Convergence Of Sequences

Let F[a, b] be the linear space of all real valued functions defined on [a, b]. A linear operator L: C[a, b] → F[a, b] is called positive (and hence monotone) on C[a, b] if L(f)≥0 whenever f≥0. There has been a considerable amount of research concerned with the convergence of sequences of the form {Ln(f)} to f where {Ln} is a sequence of positive linear operators on C[a, b].

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

2016 ◽  
Vol 56 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Hudson Akewe ◽  
Adesanmi Mogbademu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
The Common ◽  
Stability Results

Abstract In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-Kirk-Noor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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