Title :

Jordan product commuting maps with λ-Aluthge transform

Author(s) :

Chabbabi, F [Auteur]
Université de Lille, Sciences et Technologies
Mbekhta, M [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

normal
quasi-normal operators
polar decomposition
λ-Aluthge transform

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Algèbres d'opérateurs [math.OA]

English abstract : [en]

Let H and K be two complex Hilbert spaces and B(H) be the algebra of bounded linear operators from H into itself. The main purpose in this paper is to obtain a characterization of bijective maps Φ : B(H) → B(K) satisfying ...
Show more >Let H and K be two complex Hilbert spaces and B(H) be the algebra of bounded linear operators from H into itself. The main purpose in this paper is to obtain a characterization of bijective maps Φ : B(H) → B(K) satisfying the following condition Δ λ (Φ(A) • Φ(B)) = Φ(Δ λ (A • B)) for all A, B ∈ B(H), where Δ λ (T) stands the λ-Aluthge transform of the operator T ∈ B(H) and A • B = 1 2 (AB + BA) is the Jordan product of A and B. We prove that a bijective map Φ satisfies the above condition, if and only if there exists an unitary operator U : H → K, such that Φ has the form Φ(A) = UAU * for all A ∈ B(H).Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL