Characterization of linear preservers of generalized majorization on c0

Ali, Eshkaftaki Bayati; Eftekhari, Noha

doi:10.2298/fil1715979b

Cited by 3 publications

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“…In 1992, Pierce obtained a survey of linear preserver problemmas [8]. The standard work on the theory of majorization and its applications is given by Marshall and Olkin in [7] and for relative papers, see [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

On block diagonal majorization and basic sequences

Eshkaftaki

Eftekhari

2021

Filomat

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In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using block diagonal row stochastic matrices (as a special case), we define the relation < bdr on c0, which is said block diagonal majorization. We also obtain some important properties of Pbdr, the set of all bounded linear operators T : c0 ? c0; which preserve < bdr : Further, it is obtained necessary conditions for a bounded linear operator T on c0 to be a preserver of the block diagonal majorization < bdr. Also, the notion of the basic sequences correspond to block diagonal row stochastic matrices with description of some relevant examples will be discussed.

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Section: Introductionmentioning

confidence: 99%

On block diagonal majorization and basic sequences

Eshkaftaki

Eftekhari

2021

Filomat

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Linear preservers of DSS-weak majorization on discrete Lebesgue space , when I is an infinite set

Ljubenović

Rakić

Djordjević

2019

Linear and Multilinear Algebra

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Characterization of strong preserver operators of convex equivalent on the space of all real sequences tend to zero

Eftekhari¹,

Bayati²

2019

Filomat

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In this work we consider all bounded linear operators T : c 0 → c 0 that preserve convex equivalent relation ∼ c on c 0 and we denote by P ce (c 0) the set of such operators. If T strongly preserves convex equivalent, we denote them by P sce (c 0). Some interesting properties of P ce (c 0) are given. For T ∈ P ce (c 0), we show that all rows of T belong to 1 and for any j ∈ N, we have 0 ∈ Im(Te j), also there are a, b ∈ Im(Te j) such that co(Te j) = [a, b]. It is shown that all row sums of T belong to [a, b]. We characterize the elements of P ce (c 0), and some interesting results of all T ∈ P sce (c 0) are given, for example we prove that a = 0 < b or a < 0 = b. Also the elements of P sce (c 0) are characterized. We obtain the matrix representation of T ∈ P sce (c 0) does not contain any zero row. Some relevant examples are given.

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Characterization of linear preservers of generalized majorization on c0

Cited by 3 publications

References 0 publications

On block diagonal majorization and basic sequences

On block diagonal majorization and basic sequences

Linear preservers of DSS-weak majorization on discrete Lebesgue space , when I is an infinite set

Characterization of strong preserver operators of convex equivalent on the space of all real sequences tend to zero

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