1996/04/01 by S. Ferleger, Fedor Sukochev · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory #Contractible space #Mathematics #Banach space #Invertible matrix #Commutative property #Group (periodic table) #Pure mathematics #Norm (philosophy) #Linear map #Continuous linear operator #Linear operators #Discrete mathematics #Combinatorics #Mathematical analysis #Physics
paper · doi:10.1017/s0305004100074405
openalex publication_date 1996/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
For every Banach space X , denote by GL ( X ) the linear group of X , i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL ( X ) is contractible to a point if there exists a continuous map F : GL ( X ) × [0, 1] → GL ( X ) such that F ( A ,0) = A and F ( A , 1) = Id , for every A ∈ GL ( X ).