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Title: Contractive projections and Seever's identity in complex $f$-algebras (English)
Author: Hadded, Fatma
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 44
Issue: 2
Year: 2003
Pages: 203-215
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Category: math
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Summary: In this paper we give necessary and sufficient conditions in order that a contractive projection on a complex $f$-algebra satisfies Seever's identity. (English)
Keyword: vector lattice
Keyword: $\sigma$-Dedekind complete vector lattice
Keyword: Dedekind complete vector lattice
Keyword: complex $f$-algebra
Keyword: contractive projection
MSC: 06F25
MSC: 46A40
MSC: 46H05
idZBL: Zbl 1103.46024
idMR: MR2026158
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Date available: 2009-01-08T19:28:48Z
Last updated: 2020-02-20
Stable URL: http://hdl.handle.net/10338.dmlcz/119380
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Reference: [1] Bernau S.J., Huijmans C.B.: The order bidual of almost $f$-algebras and $d$-algebras.Trans. Amer. Math. Soc. 347 (1995), 4259-4274. MR 1308002
Reference: [2] Beukers F., Huijmans C.B., de Pagter B.: Unital embedding and complexification of $f$-algebras.Math. Z. 183 (1983), 131-144. MR 0701362, 10.1007/BF01187219
Reference: [3] Fremlin D.H.: Topological Riesz Spaces and Measure Theory.Cambridge University Press, 1974. Zbl 0273.46035, MR 0454575
Reference: [4] Friedman Y., Russo B.: Contractive projections on $C_{0}(K)$.Trans. Amer. Math. Soc. 273 (1982), 57-73. MR 0664029
Reference: [5] Huijsmans C.B.: The order bidual of lattice ordered algebras II.J. Operator Theory 22 (1989), 277-290. Zbl 0763.46004, MR 1043728
Reference: [6] Huijsmans C.B., de Pagter B.: Averaging operators and positive contractive projections.J. Math. Anal. Appl. 113 (1986), 163-184. Zbl 0604.47024, MR 0826666, 10.1016/0022-247X(86)90340-9
Reference: [7] Huijsmans C.B., de Pagter B.: Subalgebras and Riesz subspaces of an $f$-algebra.Proc. London Math. Soc. (3) 48 (1984), 161-174. Zbl 0534.46010, MR 0721777
Reference: [8] Huijsmans C.B., de Pagter B.: The order bidual of lattice ordered algebras.J. Funct. Anal. 59 (1984), 41-64. Zbl 0549.46006, MR 0763776, 10.1016/0022-1236(84)90052-1
Reference: [9] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North-Holland, Amsterdam, 1971.
Reference: [10] Schaefer H.H.: Banach Lattices and Positive Operators.Springer, Berlin, 1974. Zbl 0296.47023, MR 0423039
Reference: [11] Seever G.L.: Nonnegative projections on $C_{0}(X)$.Pacific J. Math. 17 (1966), 159-166. Zbl 0137.10002, MR 0192356, 10.2140/pjm.1966.17.159
Reference: [12] Triki A.: A note on averaging operators.Contemp. Math. 232 (1999), 345-348. Zbl 0946.46006, MR 1678346, 10.1090/conm/232/03410
Reference: [13] Triki A.: On algebra homomorphisms in complex almost $f$-algebras, Comment. Math. Univ. Carolinae.43.1 (2002), 23-31. MR 1903304
Reference: [14] Triki A.: When the order bidual of an $f$-algebra has a unit element.Faculté des Sciences de Tunis, preprint 2002.
Reference: [15] Zaanen A.C.: Riesz Spaces II.North-Holland, Amsterdam, 1983. Zbl 0519.46001, MR 0704021
Reference: [16] Wulbert D.E.: Averaging projections.Illinois J. Math. 13 (1969), 689-693. Zbl 0179.18201, MR 0256176, 10.1215/ijm/1256053428
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