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 preserversCalkin algebraInner productAnti-HermiticityInvertibility
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...
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关键词翻译
关键词翻译
  • 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