×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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 (∏2\(L\)∞, 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] {\scY. Gordon and D. R. Lewis}, Absolutely summing operators and local unconditional structures, Acta. 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 Lp which embed into lp, 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 Lp, 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, () · 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 Lp, 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 Lp, Ann. of math., 97, 344-373, (1973) · Zbl 0253.46049
[29] Rosenthal, H.P, A characterization of Banach spaces containing l1, (), 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.