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Title: A characterization of complex $L_1$-preduals via a complex barycentric mapping (English)
Author: Petráček, Petr
Author: Spurný, Jiří
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 57
Issue: 1
Year: 2016
Pages: 39-49
Summary lang: English
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Category: math
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Summary: We provide a complex version of a theorem due to Bednar and Lacey characterizing real $L_1$-preduals. Hence we prove a characterization of complex $L_1$-preduals via a complex barycentric mapping. (English)
Keyword: complex Banach spaces
Keyword: $L_1$-predual
Keyword: barycentric mapping
MSC: 46B25
idZBL: Zbl 06562194
idMR: MR3478337
DOI: 10.14712/1213-7243.2015.151
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Date available: 2016-04-12T05:02:52Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/144913
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Reference: [1] Alfsen E.M.: Compact Convex Sets and Boundary Integrals.Ergebnisse der Mathematik und ihrer Grenzgebiete, 57, Springer, New York, 1971. Zbl 0209.42601, MR 0445271
Reference: [2] Bednar J., Lacey H.: Concerning Banach spaces whose duals are abstract L-spaces.Pacific J. Math. 41 (1972), no. 1, 13–24. MR 0308747, 10.2140/pjm.1972.41.13
Reference: [3] Effros E.G.: On a class of complex Banach spaces.Illinois J. Math. 18 (1974), 48–59. MR 0328548
Reference: [4] Ellis A.J., Rao T.S.S.R.K., Roy A.K., Uttersrud U.: Facial characterizations of complex Lindenstrauss spaces.Trans. Amer. Math. Soc. 268 (1981), no. 1, 173–186. MR 0628453, 10.1090/S0002-9947-1981-0628453-7
Reference: [5] Fabian M., Habala P., Hájek P., Montesinos V., Zizler V.: Banach Space Theory.The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer, New York, 2011. Zbl 1229.46001, MR 2766381
Reference: [6] Hustad O.: Intersection properties of balls in complex Banach spaces whose duals are ${L_1}$-spaces.Acta Math. 132 (1974), no. 1, 283–313. MR 0388049, 10.1007/BF02392118
Reference: [7] Krause U.: Der Satz von Choquet als ein abstrakter Spektralsatz und vice versa.Math. Ann. 184 (1970), no. 4, 275–296. MR 1513280, 10.1007/BF01350856
Reference: [8] Lacey H.E.: The Isometric Theory of Classical Banach Spaces.Die Grundlehren der mathematischen Wissenschaften, 208, Springer, New York, 1974. Zbl 0285.46024, MR 0493279
Reference: [9] Lima A.: Complex Banach spaces whose duals are $L_1$-spaces.Israel J. Math. 24 (1976), no. 1, 59–72. MR 0425584, 10.1007/BF02761429
Reference: [10] Ludvík P., Spurný J.: Baire classes of complex $L_1$-preduals.Czechoslovak Math. J. 65(140) (2015), no. 3, 659–676. MR 3407598, 10.1007/s10587-015-0201-6
Reference: [11] Ludvík P., Spurný J.: Baire classes of $L_1$-preduals and $C^*$-algebras.Complex Banach spaces whose duals are $L_1$-spaces, Illinois J. Math. 58 (2014), no. 1, 97–112. MR 3331842
Reference: [12] Ludvík P., Spurný J.: Baire classes of nonseparable $L_1$-preduals.Q.J. Math. 66 (2015), no. 1, 251–263. 10.1093/qmath/hau007
Reference: [13] Ludvík P., Spurný J.: Descriptive properties of elements of biduals of Banach spaces.Studia Math. 209 (2012), no. 1, 71–99. MR 2914930, 10.4064/sm209-1-6
Reference: [14] Lukeš J., Malý J., Netuka I., Spurný J.: Integral Representation Theory.Applications to Convexity, Banach Spaces and Potential Theory, de Gruyter Studies in Mathematics, 35, Walter de Gruyter & Co., Berlin, 2010. MR 2589994
Reference: [15] Lusky W.: Every separable $L_1$-predual is complemented in a $C^*$-algebra.Studia Math. 160 (2004), no. 2, 103–116. MR 2033145, 10.4064/sm160-2-1
Reference: [16] Olsen G.H.: On the classification of complex Lindenstrauss spaces.Mathematica Scand. 35 (1974), 237–258. MR 0367626
Reference: [17] Roy A.K.: Convex functions on the dual ball of a complex Lindenstrauss space.J. London Math. Soc. (2) 20 (1979), no. 3, 529–540. MR 0561144, 10.1112/jlms/s2-20.3.529
Reference: [18] Spurný J.: Borel sets and functions in topological spaces.Acta Math. Hungar. 129 (2010), no. (1-2), 47–69. MR 2725834, 10.1007/s10474-010-9223-6
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