Some results on $\sigma$-derivations

Hosseini, Amin; Hassani, Mahmoud; Niknam, Assadollah; Hejazian, Shirin

doi:10.15352/afa/1399900196

Cited by 11 publications

(4 citation statements)

References 4 publications

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“…The following corollary provides the conditions under which a σ -derivation is zero. For more details on σ -derivations, we refer the reader to [6] and the references therein. In the following theorem, it is supposed that d 0 = I , where I is the identity mapping on A.…”

Section: Casementioning

confidence: 99%

Linear mappings satisfying some recursive sequences

Hosseini¹,

Karizaki²

2020

Turk J Math

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Let A be a unital, complex normed *-algebra with the identity element e such that the set of all algebraic elements of A is norm dense in the set of all self-adjoint elements of A and let {Dn} ∞ n=0 and {∆n} ∞ n=0 be sequences of continuous linear mappings on A satisfying    Dn+1(p) = ∑ n k=0 D n−k (p)D k (p), ∆n+1(p) = ∑ n k=0 ∆ n−k (p)D k (p), for all projections p of A and all nonnegative integers n. Moreover, suppose that D0(p) = D0(p) 2 holds for all projections p of A. Then ∆n = Cn 2 (R D 0 (e) ∆0 + L ∆ 0 (e) D0) for all n ∈ N , where Cn denotes the n th Catalan number and R D 0 (e) (a) = aD0(e) and L ∆ 0 (e) (a) = ∆0(e)a for all a ∈ A. Using this result, we present a characterization of left τ-centralizers satisfying a certain recursive relation. In addition, a characterization of generalized higher derivations is presented. Moreover, we show that higher derivations, prime higher derivations, left higher derivations, and σ-derivations are zero under certain conditions.

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Section: Casementioning

confidence: 99%

Linear mappings satisfying some recursive sequences

Hosseini¹,

Karizaki²

2020

Turk J Math

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“…As is well known, the class of derivations is a very important class of linear mappings both in theory and applications and was studied intensively. Recently, a number of authors [1,4,8,9,14] have studied various generalized notions of derivations in the context of Banach algebras. Such mappings have been extensively studied in pure algebra; cf.…”

Section: Introductionmentioning

confidence: 99%

A characterization of derivations on uniformly mean value Banach algebras

Hosseini¹

2016

Turk J Math

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In this paper, a uniformly mean value Banach algebra (briefly UMV-Banach algebra) is defined as a new class of Banach algebras, and we characterize derivations on this class of Banach algebras. Indeed, it is proved that if A is a unital UMV-Banach algebra such that either a = 0 or b = 0 whenever ab = 0 in A , and if δ : A → A is a derivation such that aδ(a) = δ(a)a for all a ∈ A , then the following assertions are equivalent: (i) δ is continuous; (ii) δ(e a) = e a δ(a) for all a ∈ A ; (iii) δ is identically zero.

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“…Let σ : A → B be a linear mapping and X be a B-bimodule. A linear mapping d : A → X is called a σ-derivation if d(ab) = d(a)σ(b) + σ(a)d(b) holds for all a, b ∈ A. Hosseini et al [4] extended this concept and defined generalized σ-derivation as follows: A linear mapping δ : A → X is called a generalized σ-derivation if δ(ab) = δ(a)σ(b) + σ(a)d(b), where d is a σ-derivation (for more details see [3], [4] and [5]).…”

Section: Introductionmentioning

confidence: 99%