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Inverses of disjointness preserving operators

About this Title

Y. A. Abramovich and A. K. Kitover

Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 143, Number 679
ISBNs: 978-0-8218-1397-3 (print); 978-1-4704-0270-9 (online)
MathSciNet review: 1639940
MSC: Primary 47B65; Secondary 46A40, 46B42, 47B33

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Table of Contents


  • 1. Setting forth the problems
  • 2. Some history
  • 3. Synopsis of the main results
  • 4. Preliminaries
  • 5. The McPolin-Wickstead and Huijsmans-de Pagter-Koldunov theorems revisited
  • 6. d-bases
  • 7. Band preserving operators and band-projections
  • 8. Central operators and problems A and B
  • 9. Range-domain exchange in the Huijsmans–de Pagter–Koldunov-theorem
  • 10. d-splitting number of disjointness preserving operators
  • 11. Essentially one-dimensional and discrete vector lattices
  • 12. Essentially constant functions and operators on $C$[0,1]
  • 13. Counterexamples
  • 14. Dedekind complete vector lattices and Problems A and B
  • 15. Generalizations to ($r_u$)-complete vector lattices
  • 16. Open problems