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Interpolation of weighted Banach lattices. A characterization of relatively decomposable Banach lattices

About this Title

Michael Cwikel, Per G. Nilsson and Gideon Schechtman

Publication: Memoirs of the American Mathematical Society
Publication Year 2003: Volume 165, Number 787
ISBNs: 978-0-8218-3382-7 (print); 978-1-4704-0385-0 (online)
MathSciNet review: 1996919
MSC: Primary 46B70; Secondary 46B42, 46E30, 46M35

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Table of Contents


  • Interpolation of weighted Banach lattices
  • 0. Introduction
  • 1. Definitions, terminology and preliminary results
  • 2. The main results
  • 3. A uniqueness theorem
  • 4. Two properties of the $K$-functional for a couple of Banach lattices
  • 5. Characterizations of couples which are uniformly Calderón-Mityagin for all weights
  • 6. Some uniform boundedness principles for interpolation of Banach lattices
  • 7. Appendix: Lozanovskii’s formula for general Banach lattices of measurable functions
  • A characterization of relatively decomposable Banach lattices
  • 1. Introduction
  • 2. Equal norm upper and lower $p$-estimates and some other preliminary results
  • 3. Completion of the proof of the main theorem
  • 4. Application to the problem of characterizing interpolation spaces