On M-ideals and o-O type spaces

• Karl-Mikael Perfekt ^[1]
  1. [1] University of Reading

     University of Reading

     Reino Unido

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 1, 2017, págs. 151-160
• Idioma: inglés
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• Resumen

  • We consider pairs of Banach spaces (M0,M) such that M0 is defined in terms of a little-o condition, and M is defined by the corresponding big-O condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual M∗∗0 of M0 is isometrically isomorphic with M. The main result of this paper is that M0 is an M-ideal in M. This has several useful consequences: M0 has Pełczýnskis properties (u) and (V), M0 is proximinal in M, and M∗0 is a strongly unique predual of M, while M0 itself never is a strongly unique predual.