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The \(L_ p\) spaces. (English) Zbl 0205.12602

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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[1] C. Bessaga and A. Pełczyński,On bases and unconditional convergence of series in Banach spaces, Studia Math.17 (1958), 151–164. · Zbl 0084.09805
[2] C. Bessaga and A. Pełczyňski,Spaces of continuous functions IV, Studia Math.19 (1960), 53–62. · Zbl 0094.30303
[3] M. M. Day,Normed linear spaces, New York, 1962. · Zbl 0100.10802
[4] N. Dunford and J. T. Schwartz,Linear operators I, New York, 1958. · Zbl 0084.10402
[5] A. Grothendieck,Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc.16 (1955). · Zbl 0064.35501
[6] A. Grothendieck,Une caracterisation vectorielle métrique des espaces L 1, Canad. J. Math.7 (1955), 552–561. · Zbl 0065.34503 · doi:10.4153/CJM-1955-060-6
[7] R. C. James,Uniformly non-square Banach spaces, Ann. of Math.80 (1964), 542–550. · Zbl 0132.08902 · doi:10.2307/1970663
[8] M. I. Kadec and A. Pełczyňski,Bases, lacunary sequences and complemented subspaces in the spaces L p, Studia Math.21 (1962), 161–176.
[9] S. Kakutani,Some characterizations of Euclidean spaces, Japan J. Math.16 (1939), 93–97. · Zbl 0022.15001
[10] V. Klee,On certain intersection properties of convex sets, Canad. J. Math.3 (1951), 272–275. · Zbl 0042.40701 · doi:10.4153/CJM-1951-031-2
[11] G. Köthe,Hebbare lokalkonvexe Raüme, Math. An.165 (1966), 181–195. · Zbl 0141.11605 · doi:10.1007/BF01343797
[12] J. Lindenstrauss,On the modulus of smoothness and divergent series in Banach spaces, Michigan Math. J.10 (1963), 241–252. · doi:10.1307/mmj/1028998906
[13] J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc.48 (1964). · Zbl 0141.12001
[14] J. Lindenstrauss,On a certain subspace of l 1, Bull. Acad. Polon. Sci.12 (1964), 539–542.
[15] J. Lindenstrauss,On the extension of operators with a finite-dimensional range, Illinois J. Math.8 (1964), 488–499. · Zbl 0132.09803
[16] J. Lindenstrauss and A. Pełczynski,Absolutely summing operators in p spaces and their applications, Studia. Math.29 (1968), 275–326. · Zbl 0183.40501
[17] J. Lindenstrauss and H. P. Rosenthal,Automorphisms in c 0,l 1,and m, Israel J. Math.7 (1969), 227–239. · Zbl 0186.18602 · doi:10.1007/BF02787616
[18] J. Lindenstrauss and D. Wulbert,On the classification of Banach spaces whose duals are L 1 spaces, J. Functional Analysis4 (1969), 332–349. · Zbl 0184.15102 · doi:10.1016/0022-1236(69)90003-2
[19] J. Lindenstrauss and M. Zippin,Banach spaces with sufficiently many Boolean algebras of Projections, J. Math. Anal. Appl.25 (1969), 309–320. · Zbl 0174.17103 · doi:10.1016/0022-247X(69)90234-0
[20] A. A. Milutin,Isomorphism of spaces of continuous functions on compacta of power continuum, Tieoria Funct., Funct. Anal. i Pril (Kharkov)2 (1966), 150–156 (Russian).
[21] A. Pełczyňski,Projections in certain Banach spaces, Studia Math.19 (1960), 209–228. · Zbl 0104.08503
[22] A. Pełczyňski,Linear extensions, linear averagings and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math., n. 58 (1968).
[23] H. P. Rosenthal,Projections onto translation-invariant subspaces of L p(G), Mem. Amer. Math. Soc.63 (1966). · Zbl 0203.43903
[24] H. P. Rosenthal, On injective Banach spaces and the spaces (\(\mu\)) for finite measures \(\mu\), (to appear). · Zbl 0179.45702
[25] W. Rudin,Trigonometric series with gaps, J. Math. Mech.9 (1960), 203–227. · Zbl 0091.05802
[26] A. Sobczyk,Projections in Minkowski and Banach spaces, Duke Math. J.8 (1941), 78–106. · JFM 67.0403.03 · doi:10.1215/S0012-7094-41-00804-9
[27] L. Tzafriri,An isomorphic characterization of L p and c 0 spaces, Studia Math.32 (1969), 286–295. · Zbl 0175.42403
[28] L. Tzafriri,Remarks on contractive projections in L p spaces, Israel J. Math.7 (1969), 9–15. · Zbl 0184.15103 · doi:10.1007/BF02771741
[29] M. Zippin,On some subspaces of Banach spaces whose duals are L 1 spaces, Proc. Amer. Math. Soc.23 (1969) 378–385. · Zbl 0184.15101
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