Approximate local isometries of derivative hardy spaces

  • A. Jiménez-Vargas
  • Takeshi Miura
Keywords: Algebraic re exivity, topological re exivity, isometry group, isometric reflection


For any 1 ≤ p ≤ ∞, let Sp (ⅅ) be the space of holomorphic functions ƒ on ⅅ such that ƒ′ belongs to the Hardy space Hp(ⅅ), with the norm ∥ƒ∥ = ∥f∥+∥ƒ′∥p. We prove that every approximate local isometry of Sp(ⅅ) is a surjective isometry and that every approximate 2-local isometry of Sp(ⅅ) is a surjective linear isometry. As a consequence, we deduce that the sets of isometric re ections and generalized bi-circular projections on Sp(ⅅ) are also topologically re exive and 2-topologically reflexive.


Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606