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Inverses of Disjointness Preserving Operators
Y. A. Abramovich, Indiana University-Purdue University, Indianapolis, IN, and A. K. Kitover, Community College of Philadelphia, PA
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Memoirs of the American Mathematical Society
2000; 162 pp; softcover
Volume: 143
ISBN-10: 0-8218-1397-8
ISBN-13: 978-0-8218-1397-3
List Price: US$54
Individual Members: US$32.40
Institutional Members: US$43.20
Order Code: MEMO/143/679
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Readership

Graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.

Table of Contents

  • Setting forth the problems
  • Some history
  • Synopsis of the main results
  • Preliminaries
  • The McPolin-Wickstead and Huijsmans-de Pagter-Koldunov Theorems revisited
  • d-bases
  • Band preserving operators and band-projections
  • Central operators and Problems A and B
  • Range-domain exchange in the Huijsmans-de Pagter-Koldunov Theorem
  • d-splitting number of disjointness preserving operators
  • Essentially one-dimensional and discrete vector lattices
  • Essentially constant functions and operators on \(C[0,1]\)
  • Counterexamples
  • Dedekind complete vector lattices and Problems A and B
  • Generalizations to \((r_u)\)-complete vector lattices
  • Open problems
  • References
  • Index
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