A solution to a problem on invertible disjointness preserving operators
HTML articles powered by AMS MathViewer
- by Yuri A. Abramovich and Arkady K. Kitover PDF
- Proc. Amer. Math. Soc. 126 (1998), 1501-1505 Request permission
Abstract:
We construct an invertible disjointness preserving operator $T$ on a normed lattice such that $T^{-1}$ is not disjointness preserving.References
- Yuri A. Abramovich, Multiplicative representation of disjointness preserving operators, Nederl. Akad. Wetensch. Indag. Math. 45 (1983), no. 3, 265–279. MR 718068
- Ju. A. Abramovič, A. I. Veksler, and A. V. Koldunov, Operators that preserve disjunction, Dokl. Akad. Nauk SSSR 248 (1979), no. 5, 1033–1036 (Russian). MR 553919
- Charalambos D. Aliprantis and Owen Burkinshaw, Positive operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985. MR 809372
- J. Araújo, E. Beckenstein, and L. Narici, When is a separating map biseparating?, Arch. Math. (Basel) 67 (1996), no. 5, 395–407. MR 1411994, DOI 10.1007/BF01189099
- J. J. Font and S. Hernández, On separating maps between locally compact spaces, Arch. Math. (Basel) 63 (1994), no. 2, 158–165. MR 1289298, DOI 10.1007/BF01189890
- C. B. Huijsmans and W. A. J. Luxemburg (eds.), Positive operators and semigroups on Banach lattices, Springer, Dordrecht, 1992. Acta Appl. Math. 27 (1992), no. 1-2. MR 1184871
- C. B. Huijsmans and B. de Pagter, Invertible disjointness preserving operators, Proc. Edinburgh Math. Soc. (2) 37 (1994), no. 1, 125–132. MR 1258036, DOI 10.1017/S0013091500018745
- C. B. Huijsmans and A. W. Wickstead, The inverse of band preserving and disjointness preserving operators, Indag. Math. (N.S.) 3 (1992), no. 2, 179–183. MR 1168345, DOI 10.1016/0019-3577(92)90006-7
- Krzysztof Jarosz, Automatic continuity of separating linear isomorphisms, Canad. Math. Bull. 33 (1990), no. 2, 139–144. MR 1060366, DOI 10.4153/CMB-1990-024-2
- A. V. Koldunov, Hammerstein operators preserving disjointness, Proc. Amer. Math. Soc. 123 (1995), no. 4, 1083–1095. MR 1212284, DOI 10.1090/S0002-9939-1995-1212284-9
- M. Meyer, Quelques propriétés des homomorphismes d’espaces vectoriels réticulés, Equipe d’Analyse Paris VI, Preprint 131, 1979.
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
- Received by editor(s): November 7, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1501-1505
- MSC (1991): Primary 47B60
- DOI: https://doi.org/10.1090/S0002-9939-98-04318-4
- MathSciNet review: 1451787