Notations and Conventions

  • Hermann König
Part of the Operator Theory: Advances and Applications book series (OT, volume 16)


By ℕ, ℤ, ℝ and ℂ we denote the natural, integer, real and complex numbers, respectively. We let ℕo ≔ ℕ ∪ {0}. Banach spaces over the field K ∈ {ℝ,ℂ} of real or complex numbers will be abbreviated by the letters X,Y,Z, operators between such spaces by R,S,T. By operators we always mean continuous linear operators between Banach spaces. The (Banach) space of continuous linear operators T from X to Y under the operator norm ‖T‖:= sup {‖Tx‖Y | ‖x‖X = 1} is denoted by L(X,Y). We let L(X) = L(X,X), BX = {x ∈ X | ‖x‖X ≤ 1} and write Id = IdX for the identity map on X. If A is a subset of X, [A] or span A denotes the closed linear hull of A in X. The topological dual of X is denoted X*(= L(X, K)) and the duality pairing written <x*,x> or x*(x) where x ∈ X, x* ∈ X*. The dual of an operator T is denoted by T*.


Banach Space Linear Operator Characteristic Function Operator Norm Complex Number 
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Copyright information

© Springer Basel AG 1986

Authors and Affiliations

  • Hermann König
    • 1
  1. 1.Mathematisches InstitutUniversität KielKiel 1Germany

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