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On Banach lattices and spaces having local unconditional structure, with applications to Lorentz function spaces. (English) Zbl 0307.46007


MSC:

46B03 Isomorphic theory (including renorming) of Banach spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A40 Ordered topological linear spaces, vector lattices
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References:

[1] Abramovich, A., Weakly compact sets in topological \(K\)-spaces, Teor. Funkciĭ. Funkcional. Anal. i Prilozen, 15, 27-35 (1972), (In Russian)
[2] Altshuler, Z.; Casazza, P. G.; Lin, B. L., On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math., 15, 140-155 (1973) · Zbl 0264.46011
[3] Bessaga, C.; Pelczynski, A., On bases and unconditional convergence of series in Banach spaces, Studia Math., 17, 151-164 (1958) · Zbl 0084.09805
[4] Bessaga, C.; Pelczynski, A., A generalization of results of R. C. James concerning absolute bases in Banach spaces, Studia Math., 17, 165-174 (1958) · Zbl 0084.10001
[5] Casazza, P. G.; Lin, B. L., On symmetric basic sequences in Lorentz sequence spaces II, Israel J. Math., 17, 191-218 (1974) · Zbl 0286.46019
[6] Dacunha-Castelle, D.; Krivine, J. L., Application des ultraproduits à l’étude des espace et des algèbres de Banach, Studia Math., 41, 315-334 (1972) · Zbl 0275.46023
[7] Davis, W. J.; Figiel, T.; Johnson, W. B.; Pelczynski, A., Factoring weakly compact operators, J. Functional Analysis, 17 (1974) · Zbl 0306.46020
[8] Dubinsky, E.; Pelczynski, A.; Rosenthal, H. P., On Banach spaces \(X\) for which (∏\(_2L\)∞, \(X) = B(L\)∞, \(X)\), Studia Math., 44, 617-648 (1972) · Zbl 0262.46018
[9] Enflo, P., Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math., 13, 281-288 (1972)
[10] Enflo, P.; Rosenthal, H. P., Some results concerning \(L^p\)(μ)-spaces, J. Functional Analysis, 14, 325-348 (1973) · Zbl 0265.46032
[11] Figiel, T., Factorization of compact operators and applications to the approximation problem, Studia Math., 45, 191-210 (1973) · Zbl 0257.47017
[12] Y. Gordon and D. R. LewisActa. Math.; Y. Gordon and D. R. LewisActa. Math. · Zbl 0291.47017
[13] Grothendieck, A., Résume de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Matem. Sao Paolo, 8, 1-79 (1956) · Zbl 0074.32303
[14] James, R. C., Super-reflexive spaces with bases, Pacific J. Math., 41, 409-419 (1972) · Zbl 0218.46011
[15] Johnson, W. B., On finite dimensional subspaces of Banach spaces with local unconditional structure, Studia Math., 51 (1974) · Zbl 0301.46012
[16] Johnson, W. B.; Odell, E., Subspaces of \(L_p\) which embed into \(l_p\), Compositio Math., 28, 37-49 (1974) · Zbl 0282.46020
[17] Johnson, W. B.; Rosenthal, H. P.; Zippin, M., On bases, finite dimensional decompositions, and weaker structures in Banach spaces, Israel J. Math., 9, 488-506 (1971) · Zbl 0217.16103
[18] Kadec, M. I.; Pelczynski, A., Bases, lacunary sequences, and complemented subspaces in the spaces \(L_p\), Studia Math., 21, 161-176 (1962) · Zbl 0102.32202
[19] Kakutani, S., Concrete representation of abstract \(L\)-spaces and the mean ergodic theorem, Ann. of Math., 42, 523-537 (1941) · JFM 67.0419.01
[20] Lindenstrauss, J.; Pelczynski, A., Absolutely summing operators in \(L_p\)-spaces and their applications, Studia Math., 29, 275-326 (1968) · Zbl 0183.40501
[21] Lindenstrauss, J.; Rosenthal, H. P., The \(L_p\) spaces, Israel J. Math., 7, 325-349 (1969) · Zbl 0205.12602
[22] Lindenstrauss, J.; Tzafriri, L., Classical Banach spaces, (Lecture Notes in Mathematics 338 (1973), Springer-Verlag: Springer-Verlag New York, Berlin) · Zbl 0478.46019
[23] Lorentz, G. G., On the theory of spaces Λ, Pacific J. Math., 1, 411-429 (1950) · Zbl 0043.11302
[24] Lozanovskii, G. J.; Mekler, A. A., Completely linear functionals and reflexivity in normed linear lattices, Izv. Vis. Ucebnik. Zav., 11, 47-53 (1967)
[25] Maurey, B., Théorèms de factorisation pour les opérateurs linéaires à valeurs dans les espaces \(L^p\), Société Mathématique de France, 11 (1974) · Zbl 0278.46028
[26] Meyer-Nieberg, P., Charakterisierung einiger lopologischer und ordnungstheoretischer Eigenschaften von Banachverbänden mit Hilfe disjunkter Folgen, Arch. Math., 24, 640-647 (1973) · Zbl 0275.46005
[27] Meyer-Nieberg, P., Zur schwachen Kompaktheit in Banachverbänden, Math. Z., 134, 303-316 (1973) · Zbl 0268.46010
[28] Rosenthal, H. P., On subspaces of \(L^p\), Ann. of Math., 97, 344-373 (1973) · Zbl 0253.46049
[29] Rosenthal, H. P., A characterization of Banach spaces containing \(l^1\), (Proc. Nat. Acad. Sciences, 71 (1974)), 2411-2413 · Zbl 0297.46013
[30] Tzafriri, L., Reflexivity in Banach lattices and their subspaces, J. Functional Analysis, 10, 1-18 (1972) · Zbl 0234.46013
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