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A solution to a problem on invertible disjointness preserving operators
Author(s):
Yuri
A.
Abramovich;
Arkady
K.
Kitover
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1501-1505.
MSC (1991):
Primary 47B60
MathSciNet review:
1451787
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Abstract:
We construct an invertible disjointness preserving operator  on a normed lattice such that  is not disjointness preserving.
References:
- [A]
- Y. A. Abramovich, Multiplicative representation of disjointness preserving operators, Netherl. Acad. Wetensch. Proc. Ser. A 86(1983), 265-279. MR 85f:47040
- [AVK]
- Y. A. Abramovich, A. I. Veksler and A. V. Koldunov, Operators preserving disjointness, Dokl. Akad. Nauk SSSR 248(1979), 1033-1036; English transl., Soviet Math. Dokl. 20 (1979), 1089-1093.MR 81e:47034
- [AB]
- C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York & London, 1985. MR 87h:47086
- [ABN]
- J. Araujo, E. Beckenstein and L. Narici, When is a separating map biseparating? Archiv der Math. 67(1996), 395-407. MR 97f:47026
- [FH]
- J. J. Font and S. Hernandez, On separating maps between locally compact spaces, Archiv der Math. 63(1994), 158-165. MR 95k:46083
- [HL]
- C. B. Huijsmans and W. A. J. Luxemburg, ed., Positive Operators and Semigroups on Banach Lattices, Kluwer, Dordrecht, 1992. MR 93e:47003
- [HP]
- C. B. Huijsmans and B. de Pagter, Invertible disjointness preserving operators, Proceed. Edinburgh. Math. Soc. (2) 37(1994), 125-132. MR 95d:47043
- [HW]
- C. B. Huijsmans and A. W. Wickstead, The inverse of band preserving and disjointness preserving operators, Indag. Math. 3(1992), 179-183. MR 94g:47047
- [J]
- K. Jarosz, Automatic continuity of separating linear isomorphisms, Canad. Math. Bull. 33(1990), 139-144. MR 92j:46049
- [K]
- A. V. Koldunov, Hammerstein operators preserving disjointness, Proc. Amer. Math. Soc. 123(1995), 1083-1095. MR 95e:47053
- [M]
- M. Meyer, Quelques propriétés des homomorphismes d'espaces vectoriels réticulés, Equipe d'Analyse Paris VI, Preprint 131, 1979.
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Additional Information:
Yuri
A.
Abramovich
Affiliation:
Department of Mathematics, Indiana University/Purdue University--Indianapolis, 402 Blackford Street, Indianapolis, Indiana 46202
Email:
yabramovich@math.iupui.edu
Arkady
K.
Kitover
Affiliation:
Department of Mathematics, Community College of Philadelphia, Philadelphia, Pennsylvania 19130
Email:
akitover@ccp.cc.pa.us
DOI:
10.1090/S0002-9939-98-04318-4
PII:
S 0002-9939(98)04318-4
Keywords:
Vector lattice,
normed lattice,
disjointness preserving operators,
band preserving operators,
invertible operators
Received by editor(s):
November 7, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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