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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)
DOI: https://doi.org/10.1090/memo/0679
MathSciNet review: 1639940
MSC: Primary 47B65; Secondary 46A40, 46B42, 47B33
Table of Contents
Chapters
- 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