Bilocal *-automorphisms of B(H) satisfying the 3-local property

Essaleh, Ahlem Ben Ali; Niazi, Mohsen; Peralta, Antonio M.

doi:10.1007/s00013-015-0723-z

Arch. Math.

2015

DOI: 10.1007/s00013-015-0723-z

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Bilocal *-automorphisms of B(H) satisfying the 3-local property

Ahlem Ben Ali Essaleh

Mohsen Niazi

Antonio M. Peralta

Abstract: Abstract. We prove that, for a complex Hilbert space H with dimension bigger or equal than three, every linear mapping T

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Weak-2-local symmetric maps on C⁎-algebras

Cabello

Peralta

2016

Linear Algebra and its Applications

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We introduce and study weak-2-local symmetric maps between C * -algebras A and B as non necessarily linear nor continuous maps ∆ : A → B such that for each a, b ∈ A and φ ∈ B * , there exists a symmetric linear map T a,b,φ : A → B, depending on a, b and φ, satisfying φ∆(a) = φT a,b,φ (a) and φ∆(b) = φT a,b,φ (b). We prove that every weak-2-local symmetric map between C * -algebras is a linear map. Among the consequences we show that every weak-2-local * -derivation on a general C * -algebra is a (linear) * -derivation. We also establish a 2-local version of the Kowalski-S lodkowski theorem for general C *algebras by proving that every 2-local * -homomorphism between C * -algebras is a (linear) * -homomorphism.

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Weak-2-local symmetric maps on C⁎-algebras

Cabello

Peralta

2016

Linear Algebra and its Applications

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On a generalized Šemrl’s theorem for weak 2-local derivations on $B(H)$

Cabello¹,

Peralta²

2017

Banach J. Math. Anal.

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Bilocal *-automorphisms of B(H) satisfying the 3-local property

Abstract: Abstract. We prove that, for a complex Hilbert space H with dimension bigger or equal than three, every linear mapping T

Cited by 2 publications

References 12 publications

Weak-2-local symmetric maps on C⁎-algebras

Weak-2-local symmetric maps on C⁎-algebras

On a generalized Šemrl’s theorem for weak 2-local derivations on $B(H)$

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