1. Linear maps preserving A-unitary operators
- Creator:
- Chahbi, Abdellatif, Kabbaj, Samir, and Charifi, Ahmed
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- linear preserver problem and semi-inner produst
- Language:
- English
- Description:
- Let H be a complex Hilbert space, A a positive operator with closed range in B(H) and BA(H) the sub-algebra of B(H) of all A-self-adjoint operators. Assume ϕ: BA(H) onto itself is a linear continuous map. This paper shows that if ϕ preserves A-unitary operators such that ϕ(I) = P then ψ defined by ψ(T ) = P ϕ(P T ) is a homomorphism or an anti-homomorphism and ψ(T ♯ ) = ψ(T ) ♯ for all T ∈ BA(H), where P = A +A and A + is the Moore-Penrose inverse of A. A similar result is also true if ϕ preserves A-quasi-unitary operators in both directions such that there exists an operator T satisfying P ϕ(T ) = P.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public