Anti-G-Hermiticity Preserving Linear Map That Preserves Strongly the Invertibility of Calkin Algebra Elements
 作者： Jay G. Buscano and Jose Tristan F. Reyes 刊名： Manila Journal of Science, 2018, Vol.11 来源数据库： De La Salle University 关键词： Linear preservers;  Calkin algebra;  Inner product;  Anti-Hermiticity;  Invertibility; 原始语种摘要： A linear map ψ : X → Y of algebras X and Y preserves strongly invertibility if ψ(x−1) = ψ(x)−1 for all x ∈ X−1, where X−1 denotes the set of invertible elements of X. Let B(H) be the Banach algebra of all bounded linear operators on a separable complex Hilbert space H with dim H = ∞. A Calkin algebra C(H) is the quotient of B(H) by K(H), the ideal of compact operators on H. An element A + K(H) ∈ C(H) is said to be anti-G-Hermitian if (A + K(H))# = −A + K(H), where the # -operation is an involution on C(H). A linear map  : C(H) → C(H) preserves anti-G-Hermiticity if  (A + K(H))# = − (A + K(H)) for all anti-G-Hermitian element A + K(H) ∈ C(H). In this paper, we characterize the continuous unital linear map  : C(H) → C(H) induced by the essentially antiG-Hermiticity preserving linear map... φ : B(H) → B(H) that preserves strongly the invertibility of operators on H. We also take a look at the linear preserving properties of this induced map and other linear preservers on C(H). The discussion is in the context of G-operators, that is, linear operators on H with respect to a fixed but arbitrary positive definite Hermitian operator G ∈ B(H)−1.

• 理想　定的
• operators　操作符
• algebra　代数学
• preserving　保藏
• Hermitian　conjugate[数](矩阵的)厄密共轭
• preserves　蜜饯
• invertibility　可逆性
• arbitrary　任意的
• separable　可分的
• definite　定的
• ideal　定的