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The Banach spaces $C\left( K \right)$ and $L^p \left( \mu \right)^1$
Author(s):
Haskell P.
Rosenthal
Journal:
Bull. Amer. Math. Soc.
81
(1975),
763-781.
MSC (1970):
Primary 43A15, 46C05, 46E15, 46E30, 46G10
MathSciNet review:
0380381
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Additional information
References:
- 1.
- G. F. Bachelis and S. Ebenstein, On Λ(P) sets, Pacific J. Math. 54 (1974), 35-38. MR 383005
- 2.
- J. Bretagnolle, D. Dacunha-Castelle and J.-L. Krivine, Lois stables et espaces L, Ann. Inst. H. Poincaré, Sect. B (N.S.) 2 (1965/66), 231-259. MR 34 #3605. MR 203757
- 3.
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504. MR 34 #8456. MR 208647
- 4.
- J. Diestel and J. J. Uhl, Jr., The Radon-Nikodym theorem for Banach space valued measures, Rocky Mountain J. Math. (to appear). MR 399852
- 5.
- S. Z. Ditor, On a lemma of Milutin concerning averaging operators in continuous function spaces, Trans. Amer. Math. Soc. 149 (1970), 443-452. MR 435921
- 6.
- E. L. Dubinski, A. Pełczyński, and H. P. Rosenthal, On Banach spaces X for which Π, Studia Math. 44 (1972), 617-648.
- 7.
- N. Dunford and J. T. Schwartz, Linear operators. I. General theory, Pure and Appl. Math., vol. 7, Interscience, New York, London, 1958. MR 22 #8302. MR 117523
- 8.
- P. Enflo and H. P. Rosenthal, Some results concerning L, J. Functional Analysis 14 (1973), 325-348. MR 350402
- 9.
- J. L. B. Gamlen and R. J. Gaudet, On subsequences of the Haar system in L, Israel J. Math. 15 (1973), 404-413. MR 328575
- 10.
- A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. MR 15, 438. MR 58866
- 11.
- A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1956), 1-79. MR 20 #1194. MR 94682
- 12.
- J. Hagler, Embeddings of L, Thesis, University of California, Berkeley, Calif., 1972.
- 13.
- J. Hagler and C. Stegall, Banach spaces whose duals contain complemented subspaces isomorphic to C[0, 1], J. Functional Analysis 13 (1973), 233-251. MR 350381
- 14.
- W. B. Johnson and E. Odell, Subspaces of L, Compositio Math. 28 (1974), 37-49. MR 352938
- 15.
- W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506. MR 43 #6702. MR 280983
- 16.
- W. B. Johnson and M. Zippin, On subspaces of quotients of $(\sum G\sbn)\sblp$ and $(\sum G\sbn)\sb{c\sb{0}}$, Israel J. Math. 13 (1972), 311-316. MR 331023
- 17.
- W. B. Johnson and M. Zippin, Separable L, Israel J. Math. 16 (1973), 198-202. MR 338745
- 18.
- M. Ǐ. Kadeć and A. Pełczyński, Bases, lacunary sequences and complemented subspaces in the spaces L, Studia Math. 21 (1961/62), 161-176. MR 27 #2851.
- 19.
- G. Köthe, Hebbare lokalkonvexe Räume, Math. Ann. 165 (1966), 181-195. MR 33 #4651. MR 196464
- 20.
- S. Kwapień, On a theorem of L. Schwartz and its applications to absolutely summing operators, Proc. Internat. Colloq. on Nuclear Spaces and Ideals in Operator Algebras (Warsaw, 18-25 June, 1969), Studia Math. 38 (1970), 193-201. MR 43 #3822. MR 278090
- 21.
- D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to l, J. Functional Analysis 12 (1973), 177-187. MR 342987
- 22.
- J. Lindenstrauss, On the extension of operators with a finite-dimensional range, Illinois J. Math. 8 (1964), 488-499. MR 29 #6317. MR 169062
- 23.
- J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in L, Studia Math. 29 (1968), 275-326. MR 37 #6743. MR 231188
- 24.
- J. Lindenstrauss and H. P. Rosenthal, The ℒ, Israel J. Math. 7 (1969), 325-349. MR 42 #5012. MR 270119
- 25.
- J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., vol. 338, Springer-Verlag, New York, 1973. MR 415253
- 26.
- B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces L, Société Mathematique de France, Astérisque 11 (1974), 1-163. MR 344931
- 27.
- A. A. Milutin, Isomorphism of spaces of continuous functions on compacta having the power of the continuum, Teor. Funkcii Funkcional. Anal. i Priložen 2 (1966), 150-156. (Russian) MR 206695
- 28.
- R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. 34 (1932), 241-264.
- 29.
- A. Pełczyński, On Banach spaces containing L, Studia Math. 30 (1968), 231-246. MR 38 #521.
- 30.
- A. Pełczyński, On C(S)-subspaces of separable Banach spaces, Studia Math. 31 (1968), 513-522. MR 38 #2578; erratum, 39, p. 1593. MR 234261
- 31.
- A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228. MR 23 #A3441. MR 126145
- 32.
- A. Pełczyński and H. P. Rosenthal, Localization techniques in L, Studia Math. 52 (1975), 263-289.
- 33.
- H. P. Rosenthal, On factors of C([0, 1]) with non-separable dual, Israel J. Math. 13 (1972), 361-378. MR 388063
- 34.
- H. P. Rosenthal, On infective Banach spaces and the spaces L, Acta Math. 124 (1970), 205-248. MR 41 #2370. MR 257721
- 35.
- H. P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13-36. MR 42 #5015. MR 270122
- 36.
- H. P. Rosenthal, On subspaces of L, Ann. of Math. (2) 97 (1973), 344-373. MR 47 #784. MR 312222
- 37.
- H. P. Rosenthal, On the subspaces of L, Israel J. Math. 8 (1970), 273-303. MR 42 #6602. MR 271721
- 38.
- H. P. Rosenthal, On the span in L. II, Proc. 6th Berkeley Sympos. on Mathematical Statistics and Probability, vol. 2, 1972, pp. 149-167. MR 440354
- 39.
- H. P. Rosenthal, Some applications of p-summing operators to Banach space theory, Studia Math. (to appear). MR 430749
- 40.
- G. Schechtman, A remark on unconditional basic sequences in L, Israel J. Math. appear).
- 41.
- C. Stegall, Banach spaces whose duals contain l, Trans. Amer. Math. Soc. 176 (1973), 463-477. MR 47 #3953. MR 315404
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Additional Information:
DOI:
10.1090/S0002-9904-1975-13824-9
PII:
S 0002-9904(1975)13824-9
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