Sundual characterizations of the translation group of ${\mathbb R}$
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- by Frances Y. Jackson and W. A. J. Luxemburg PDF
- Proc. Amer. Math. Soc. 131 (2003), 185-199 Request permission
Abstract:
We characterize the first three sundual spaces of ${C_0(\mathbb R)}$, with respect to the translation group of ${\mathbb R}$.References
- Ando, T. Banachverbände und positive Projektionen. Math. Z. 109 (1969), 121–130.
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- Van Neerven, Jan. The adjoint of a semigroup of operators. Springer Verlag, Berlin, Heidelberg (1992).
- Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
- Kakutani, S. Two fixed-point theorems concerning bicompact convex sets. Proc. Imp. Acad. Tokyo 19 (1943), 269–271.
- Louis Weisner, Condition that a finite group be multiply isomorphic with each of its irreducible representations, Amer. J. Math. 61 (1939), 709–712. MR 32, DOI 10.2307/2371325
- W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. Vol. I, North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1971. MR 0511676
- Markov, A. Quelques théorèmes sur les ensembles abeliens. Doklady Akad. Nauk SSSR (N.S.) 10 (1936), 311–314.
- Ben de Pagter, A Wiener-Young type theorem for dual semigroups, Acta Appl. Math. 27 (1992), no. 1-2, 101–109. Positive operators and semigroups on Banach lattices (Curaçao, 1990). MR 1184882, DOI 10.1007/BF00046641
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- Jean-Paul Pier, Amenable locally compact groups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 767264
- Plessner, A. Eine Kennzeichnung der totalstetigen Funktionen. Math, J. für Reine und Angew. Math. 60 (1929), 26–32.
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
- A. C. Zaanen, Riesz spaces. II, North-Holland Mathematical Library, vol. 30, North-Holland Publishing Co., Amsterdam, 1983. MR 704021
Additional Information
- Frances Y. Jackson
- Affiliation: California Institute of Technology, Mathematics 253-37, Pasadena, California 91125-0087
- W. A. J. Luxemburg
- Affiliation: California Institute of Technology, Mathematics 253-37, Pasadena, California 91125-0087
- Email: lux@caltech.edu
- Received by editor(s): July 7, 2000
- Received by editor(s) in revised form: August 21, 2001
- Published electronically: May 9, 2002
- Communicated by: David R. Larson
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 185-199
- MSC (1991): Primary 47D03; Secondary 46Exx
- DOI: https://doi.org/10.1090/S0002-9939-02-06632-7
- MathSciNet review: 1929038