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Characterization of the duals of lattices of continuous functions with respect to disjointness preserving groups
Author(s):
Andrey
Y.
Biyanov
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2571-2579.
MSC (1991):
Primary 47D03, 46B10, 46E05, 47B65
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Abstract:
The duals of  and ![$C[a, b]$](/proc/1997-125-09/S0002-9939-97-03064-5/gif-abstract/img3.gif) with respect to disjointness preserving groups are characterized. A. Plessner's result (1929) about the translation group is extended. A Wiener-Young type theorem for disjointness preserving groups is obtained.
References:
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- B. de Pagter, A Wiener-Young type theorems for dual semigroups, Positive Operators and Semigroups on Banach Lattices (C. B. Huijsmans and W. A. J. Luxemburg, eds.), Kluwer Academic Publisher, Dordrecht, The Netherlands, 1992, pp. 101-109. MR 93j:47059
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- N. Dunford and T. Schwartz, Linear operators, Interscience Publishers, Inc., New York, 1958. MR 22:8302
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- W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces I, North-Holland, Amsterdam, 1971. MR 58:23483
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- P. Meyer-Nieberg, Banach lattices, Springer-Verlag, Berlin, 1991. MR 93f:46025
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- A. Plessner, Eine Kennzeichnung der totalstetigen Funktionen, J. Reine Angew. Math. 60 (1929), 26-32.
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Additional Information:
Andrey
Y.
Biyanov
Affiliation:
California Institute of Technology, 253-37, Caltech, Pasadena, California 91125
Address at time of publication:
155 Lexington St. \#33, Auburndale, MA 02166
Email:
abiyanov@cco.caltech.edu, biyanov@msn.com
DOI:
10.1090/S0002-9939-97-03064-5
PII:
S 0002-9939(97)03064-5
Keywords:
$C_{0}$-group,
disjointness preserving operator,
group dual,
flow,
cocycle
Received by editor(s):
September 2, 1994
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
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