Characterizations of linear mappings through zero products or zero Jordan products

An, Guangyu; Li, Jiankui

doi:10.13001/1081-3810.3090

Cited by 13 publications

(4 citation statements)

References 29 publications

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“…In [4], Barari et.al., characterized linear maps on standard operator algebras by action on zero products. Since then many authors have been studied linear maps on ring and (Banach) algebras through zero products, and different results have been obtained; for instance, see [2,3,4,5,16,17] and the references therein…”

Section: A Zivari-kazempouri and A Minapoormentioning

confidence: 99%

Jordan and local multipliers on certain Banach algebras are multipliers

Zivari-Kazempour

Minapoor

2023

Preprint

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‎In this paper‎, ‎we prove that every continuous Jordan multiplier T from a‎ C*-algebra or group algebra A into a Banach A-bimodule X is exact a multiplier‎. We also characterize a continuous linear map on C*-algebras and standard operator algebra‎s ‎through the action on zero products‎. ‎Additionally‎, ‎we show that every continuous local multiplier T from a Banach algebra A with the property $(\mathbb{B})$ into a Banach A-bimodule X is a multiplier‎. 2010 Mathematics Subject Classification. Primary 47B47, 47B49 Secondary 15A86, 46H25.

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Section: A Zivari-kazempouri and A Minapoormentioning

confidence: 99%

Jordan and local multipliers on certain Banach algebras are multipliers

Zivari-Kazempour

Minapoor

2023

Preprint

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“…In [3], we give a characterization of (m, n)-Jordan derivable mappings at zero on some algebras when n = 0 and m = 0. In this section, we assume that m, n are two positive numbers and study the propositions of (m, n)-Jordan derivable mappings at zero.…”

Section: (M N)-jordan Derivable Mappings At Zero On Some Algebrasmentioning

confidence: 99%

Characterizations of $(m,n)$-Jordan derivations on some algebras

An,

2018

Preprint

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Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mappingIn this paper, we prove that every (m, n)-Jordan derivation from a C * -algebra into its Banach bimodule is zero. An additive mappingfor each A and B in R with AB = BA = W . We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U = A M N B is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.

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“…Case 2 A ∼ = M n (B)(n ≥ 2), where B is also a von Neumann algebra. By [1,Theorem 2.3], ∆ is a generalized derivation with ∆(I) in the center. That is to say, ∆ is a sum of a derivation and a centralizer.…”

Section: Denote the Restriction Of ∆ Tomentioning

confidence: 99%

Characterizations of Centralizers and Derivations on Some Algebras

He¹,

Li²,

Qian³

2017

Journal of the Korean Mathematical Society

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Abstract. A linear mapping φ on an algebra A is called a centralizable mapping at G ∈ A if φ(AB) = φ(A)B = Aφ(B) for each A and B in A with AB = G, and φ is called a derivable mapping at G ∈ A if φ(AB) = φ(A)B + Aφ(B) for each A and B in A with AB = G. A point G in A is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at G is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.

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Characterizations of linear mappings through zero products or zero Jordan products

Cited by 13 publications

References 29 publications

Jordan and local multipliers on certain Banach algebras are multipliers

Jordan and local multipliers on certain Banach algebras are multipliers

Characterizations of $(m,n)$-Jordan derivations on some algebras

Characterizations of Centralizers and Derivations on Some Algebras

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