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Title: The order $\sigma $-complete vector lattice of AM-compact operators (English)
Author: Aqzzouz, Belmesnaoui
Author: Nouira, Redouane
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 59
Issue: 3
Year: 2009
Pages: 827-834
Summary lang: English
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Category: math
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Summary: We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice $E$ into a Banach lattice $F$ is an order $\sigma $-complete vector lattice. (English)
Keyword: AM-compact operator
Keyword: order continuous norm
Keyword: discrete vector lattice
MSC: 46A40
MSC: 46B40
MSC: 46B42
MSC: 47B07
MSC: 47B60
idZBL: Zbl 1222.47063
idMR: MR2545658
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Date available: 2010-07-20T15:42:06Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/140518
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Reference: [1] Abramovich, Y. A., Wickstead, A. W.: Solutions of several problems in the theory of compact positive operators.Proc. Amer. Math. Soc. 123 (1995), 3021-3026. Zbl 0860.47023, MR 1283534, 10.1090/S0002-9939-1995-1283534-8
Reference: [2] Aliprantis, C. D., Burkinshaw, O.: Locally solid Riesz spaces.Academic Press (1978). Zbl 0402.46005, MR 0493242
Reference: [3] Aliprantis, C. D., Burkinshaw, O.: Positive compact operators on Banach lattices.Math. Z. 174 (1980), 289-298. Zbl 0425.46015, MR 0593826, 10.1007/BF01161416
Reference: [4] Aliprantis, C. D., Burkinshaw, O.: On weakly compact operators on Banach lattices.Proc. Amer. Math. Soc. 83 (1981), 573-578. Zbl 0452.47038, MR 0627695, 10.1090/S0002-9939-1981-0627695-X
Reference: [5] Aqzzouz, B., Nouira, R.: Les opérateurs précompacts sur les treillis vectoriels localement convexes-solides.Sci. Math. Jpn. 57 (2003), 279-256. MR 1959985
Reference: [6] Chen, Z. L., Wickstead, A. W.: Vector lattices of weakly compact operators on Banach lattices.Trans. Amer. Math. Soc. 352 (1999), 397-412. MR 1641095, 10.1090/S0002-9947-99-02431-9
Reference: [7] Fremlin, D. H.: Riesz spaces with the order continuity property I.Proc. Cambr. Phil. Soc. 81 (1977), 31-42. Zbl 0344.46019, MR 0425572, 10.1017/S0305004100000244
Reference: [8] Krengel, U.: Remark on the modulus of compact operators.Bull. Amer. Math. Soc. 72 (1966), 132-133. Zbl 0135.36302, MR 0190752, 10.1090/S0002-9904-1966-11452-0
Reference: [9] Meyer-Nieberg, P.: Banach lattices.Universitext. Springer-Verlag, Berlin (1991). Zbl 0743.46015, MR 1128093
Reference: [10] Robertson, A. P., Robertson, W.: Topological vector spaces.2$^{ {nd}}$ ed., Cambridge University Press, London (1973). Zbl 0251.46002, MR 0350361
Reference: [11] Wickstead, A. W.: Dedekind completeness of some lattices of compact operators.Bull. Polish Acad. of Sci. Math. 43 (1995), 297-304. Zbl 0847.47025, MR 1414786
Reference: [12] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab theorems.Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752
Reference: [13] Zaanen, A. C.: Riesz spaces II.North Holland Publishing Company (1983). Zbl 0519.46001, MR 0704021
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