Topological reflexivity of isometries on algebras of matrix-valued Lipschitz maps
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2023Abstract
Let X and Y be compact metric spaces and let Mn(C) be the Banach algebra of all nxn complex matrices. We prove that the set of all unital surjective linear isometries from Lip(X,Mn(C)) to Lip(Y,Mn(C)), whenever both spaces are endowed with the sum norm, is topologically reflexive.
Palabra/s clave
Algebraic reflexivity
Topological reflexivity
Surjective linear isometry
Vector-valued Lipschitz map