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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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References:

[1] Bessaga, C.; Pełczyński, A., On bases and unconditional convergence of series in Banach spaces, Studia Math., 17, 151-164 (1958) · Zbl 0084.09805
[2] Bessaga, C.; Pełczyňski, A., Spaces of continuous functions IV, Studia Math., 19, 53-62 (1960) · 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] Grothendieck, A., Une caracterisation vectorielle métrique des espaces L^1, Canad. J. Math., 7, 552-561 (1955) · Zbl 0065.34503
[7] James, R. C., Uniformly non-square Banach spaces, Ann. of Math., 80, 542-550 (1964) · Zbl 0132.08902
[8] Kadec, M. I.; Pełczyňski, A., Bases, lacunary sequences and complemented subspaces in the spaces L_p, Studia Math., 21, 161-176 (1962) · Zbl 0102.32202
[9] Kakutani, S., Some characterizations of Euclidean spaces, Japan J. Math., 16, 93-97 (1939) · Zbl 0022.15001
[10] Klee, V., On certain intersection properties of convex sets, Canad. J. Math., 3, 272-275 (1951) · Zbl 0042.40701
[11] Köthe, G., Hebbare lokalkonvexe Raüme, Math. An., 165, 181-195 (1966) · Zbl 0141.11605
[12] Lindenstrauss, J., On the modulus of smoothness and divergent series in Banach spaces, Michigan Math. J., 10, 241-252 (1963) · Zbl 0115.10001
[13] J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc.48 (1964). · Zbl 0141.12001
[14] Lindenstrauss, J., On a certain subspace of l_1, Bull. Acad. Polon. Sci., 12, 539-542 (1964) · Zbl 0133.06604
[15] Lindenstrauss, J., On the extension of operators with a finite-dimensional range, Illinois J. Math., 8, 488-499 (1964) · Zbl 0132.09803
[16] Lindenstrauss, J.; Pełczynski, A., Absolutely summing operators in ℒ_p spaces and their applications, Studia. Math., 29, 275-326 (1968) · Zbl 0183.40501
[17] Lindenstrauss, J.; Rosenthal, H. P., Automorphisms in c_0,l_1,and m, Israel J. Math., 7, 227-239 (1969) · Zbl 0186.18602
[18] Lindenstrauss, J.; Wulbert, D., On the classification of Banach spaces whose duals are L_1 spaces, J. Functional Analysis, 4, 332-349 (1969) · Zbl 0184.15102
[19] Lindenstrauss, J.; Zippin, M., Banach spaces with sufficiently many Boolean algebras of Projections, J. Math. Anal. Appl., 25, 309-320 (1969) · Zbl 0174.17103
[20] Milutin, A. A., Isomorphism of spaces of continuous functions on compacta of power continuum, Tieoria Funct., Funct. Anal. i Pril (Kharkov), 2, 150-156 (1966)
[21] Pełczyňski, A., Projections in certain Banach spaces, Studia Math., 19, 209-228 (1960) · 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). · Zbl 0165.14603
[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 ℒ_∞ (μ) for finite measures μ, (to appear). · Zbl 0207.42803
[25] Rudin, W., Trigonometric series with gaps, J. Math. Mech., 9, 203-227 (1960) · Zbl 0091.05802
[26] Sobczyk, A., Projections in Minkowski and Banach spaces, Duke Math. J., 8, 78-106 (1941) · Zbl 0025.06304
[27] Tzafriri, L., An isomorphic characterization of L_pand c_0spaces, Studia Math., 32, 286-295 (1969) · Zbl 0175.42403
[28] Tzafriri, L., Remarks on contractive projections in L_p spaces, Israel J. Math., 7, 9-15 (1969) · Zbl 0184.15103
[29] Zippin, M., On some subspaces of Banach spaces whose duals are L_1spaces, Proc. Amer. Math. Soc., 23, 378-385 (1969) · Zbl 0184.15101
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