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Compact operators in Banach lattices. (English) Zbl 0438.47042

MSC:
47B60 Linear operators on ordered spaces
46B42 Banach lattices
46A40 Ordered topological linear spaces, vector lattices
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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[1] T. Andô,On compactness of integral operators, Indag. Math.24 (1962), 235–239. · Zbl 0100.11201
[2] J. Bourgain, D. H. Fremlin and M. Talagrand,Pointwise compact sets of Baire measurable functions, Amer. J. Math. (to appear). · Zbl 0413.54016
[3] O. Burkinshaw and P. Dodds,Disjoint sequences, compactness and semi-reflexivity in locally convex Riezz spaces. Illinois J. Math.21 (1977), 759–775. · Zbl 0434.46007
[4] P. G. Dodds,O-weakly compact mappings in Riesz space, Trans. Amer. Math. Soc.214 (1975), 389–402. · Zbl 0313.46011
[5] P. G. Dodds,Sequential convergence in the order duals of certain classes of Riesz spaces, Trans. Amer. Math. Soc.203 (1975), 391–403. · Zbl 0276.46008 · doi:10.1090/S0002-9947-1975-0358282-0
[6] P. G. Dodds,Indices for Banach lattices, Proc. Acad. Sci. AmsterdamA 80 (1977), 73–86. · Zbl 0347.46005
[7] D. H. Fremlin,Topological Riesz Spaces and Measure Theory, Cambridge University Press, 1974. · Zbl 0273.46035
[8] D. H. Fremlin,A positive compact operator, Manuscripta Math.15 (1975), 323–327. · Zbl 0318.47013 · doi:10.1007/BF01486602
[9] J. J. Grobler,Compactness conditions for integral operators in Banach function space, Proc. Acad. Sci. AmsterdamA83 (1970), 287–294. · Zbl 0203.14201
[10] J. J. Grobler,Indices for Banach function spaces, Math. Z.145 (1975), 99–109. · Zbl 0307.46023 · doi:10.1007/BF01214774
[11] A. Grothendieck,Sur les applications linéaires faiblement compactes d’espaces du type C(K), Canad. J. Math.5 (1953), 129–173. · Zbl 0050.10902 · doi:10.4153/CJM-1953-017-4
[12] M. A. Krasnoselskii, P. O. Zabreiko, E. I. Pustylnik and P. E. Sobolevskii,Integral Operators in Spaces of Summable Functions, Noordhoff I. P., Leyden, 1976.
[13] W. A. J. Luxemburg and A. C. Zaanen,Compactness of integral operators in Banach function spaces, Math. Ann.149 (1963), 150–180. · Zbl 0106.30804 · doi:10.1007/BF01349240
[14] W. A. J. Luxemburg and A. C. Zaanen,Notes on Banach function spaces, Note VIA 66 (1963), 665–681. · Zbl 0117.08002
[15] W. A. J. Luxemburg and A. C. Zaanen,Riesz Spaces I, North-Holland Mathematical Library, Amsterdam, 1972.
[16] B. Maurey,Type et cotype dans les espaces munis de structure locales inconditionelles, Séminaire Maurey-Schwartz, 1973–1974.
[17] P. Meyer-Nieberg,Zur schwachen Kompaktheit in Banachverbänden, Math. Z.134 (1973), 303–315. · Zbl 0268.46010 · doi:10.1007/BF01214694
[18] P. Meyer-Nieberg,Über Klassen schwach kompakter Operatoren in Banachverbänden, Math. Z.138 (1974), 145–159. · Zbl 0291.47020 · doi:10.1007/BF01214230
[19] P. Meyer-Nieberg,Kegel p-absolutsummierende und p-beschränkende Operatoren (to appear). · Zbl 0439.47025
[20] R. J. Nagel and U. Schlotterbeck,Integralderstellung regulärer Operatoren auf Banachverbänden, Math. Z.127 (1972), 293–300. · Zbl 0234.47036 · doi:10.1007/BF01114932
[21] R. J. Nagel and U. Schlotterbeck,Kompaktheit von Integral operatoren auf Banachverbänden, Math. Ann.202 (1973), 301–306. · Zbl 0236.47038 · doi:10.1007/BF01433460
[22] R. E. A. C. Paley,Some theorems on abstract spaces, Bull. Amer. Math. Soc. (1936), 235–240. · Zbl 0014.06704
[23] H. R. Pitt,A note on bilinear forms, J. London Math. Soc.11 (1936), 174–180. · Zbl 0014.31201 · doi:10.1112/jlms/s1-11.3.174
[24] H. P. Rosenthal,On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from L p (\(\mu\)) to L v (v), J. Functional Analysis2 (1969), 176–214. · Zbl 0185.20303 · doi:10.1016/0022-1236(69)90011-1
[25] H. H. Schaeffer,Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
[26] P. C. Shields,Weakly compact operators on spaces of summable functions, Proc. Amer. Math. Soc.37 (1973), 456–458. · Zbl 0264.47033 · doi:10.1090/S0002-9939-1973-0315506-7
[27] T. Shimogaki,Exponents of norms in semi-ordered linear spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom Phys.13 (1965), 135–140. · Zbl 0127.06401
[28] S. Simons,On the Dunford-Pettis property and Banach spaces that contain c 0 , Math. Ann.216 (1975), 225–231. · Zbl 0301.46011 · doi:10.1007/BF01430962
[29] A. C. Zaanen,Integral transformations and their resolvents in orlicz and Lebesgue spaces, Compositio Math.10 (1952), 56–94. · Zbl 0046.33901
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