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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): Sylvie Guerre-Delabri\`ere
Title: Classical sequences in Banach spaces
Additional book information: Marcel Dekker, Inc., New York, 1992, xiv + 207 pp., US$99.75. ISBN 0-8247-8723-4


References:

[1]
D. Aldous, Subspaces of $ {L_1}$ via random measures, Trans. Amer. Math. Soc. 267 (1981), 445-463. MR 626483 (83b:46025)

[2]
S. Banach, Théorie des opérations linéaires, Warszawa, 1932.

[3]
C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. MR 0115069 (22:5872)

[4]
A. Brunel and L. Sucheston, J-convexity and ergotic super-properties of Banach spaces, Trans. Amer. Math. Soc. 204 (1975), 79-90. MR 0380361 (52:1261)

[5]
D. L. Burkholder, A nonlinear partial differential equation and the unconditional constant of the Haar system in $ {L^p}$, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 591-595. MR 670133 (83j:60045)

[6]
-, Boundary value problems and sharp inequalities for martingale transforms, Ann. of Probab. 12 (1984), 647-701. MR 744226 (86b:60080)

[7]
P. G. Casazza, Some questions arising from the homogeneous Banach space problem, Banach Spaces (B-L. Lin and W. B. Johnson, eds.) Contemp. Math. vol. 144, Amer. Math. Soc., Providence, RI, 1993, pp. 35-52. MR 1209445 (93j:46016)

[8]
P. G. Casazza and T. Shura, Tsirelson's space, Lecture Notes in Math., vol. 1363, Springer-Verlag, New York, 1989. MR 981801 (90b:46030)

[9]
A. Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Sympos. on Linear Spaces, Jerusalem, 1961, pp. 123-160. MR 0139079 (25:2518)

[10]
P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309-317. MR 0402468 (53:6288)

[11]
T. Figiel and W. B. Johnson, A uniformly convex Banach space which contains no $ {l_p}$, Composito Math. 29 (1974), 179-190. MR 0355537 (50:8011)

[12]
W. T. Gowers, On the hyperplane problem, preprint.

[13]
-, A Banach space not containing $             {c_0}$, $ {l_1}$ or a reflexive subspace, preprint.

[14]
-, A new dichotomy for Banach spaces, preprint.

[15]
-, A solution to the Schroeder-Bernstein problem for Banach spaces, preprint.

[16]
W. T. Gowers and B. Maurey, The unconditional basic sequence problem, preprint. MR 1201238 (94k:46021)

[17]
A. Grothendieck, Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc., vol. 16, Amer. Math. Soc., Providence, RI, 1955. MR 0075539 (17:763c)

[18]
S. Guerre and M. Levy, Espaces $             {l_p}$ dans les sons-espaces de $ {L_1}$, Trans. Amer. Math. Soc. 279 (1983), 611-616. MR 709571 (85d:46033)

[19]
R. C. James, Bases and reflexivity of Banach spaces, Ann. of Math. (2) 52 (1950), 518-527. MR 0039915 (12:616b)

[20]
-, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542-550. MR 0173932 (30:4139)

[21]
-, A separable somewhat reflexive Banach space with non-separable dual, Bull. Amer. Math. Soc. (N.S.) 80 (1974), 738-743. MR 0417763 (54:5811)

[22]
M. I. Kadec and A. Pelczynski, Bases, lacunary sequences, and complemented subspaces of the space $ {L_p}$, Studia Math. 21 (1962), 161-176. MR 0152879 (27:2851)

[23]
R. Komorowski and N. Tomczak-Jaegermann, Banach spaces without local unconditional structure, preprint. MR 1324462 (96g:46007)

[24]
J. L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. (2) 104 (1976), 1-29. MR 0407568 (53:11341)

[25]
J. L. Krivine and B. Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), 273-295. MR 636897 (83a:46030)

[26]
J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1972), 263-269. MR 0276734 (43:2474)

[27]
-, On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379-390. MR 0313780 (47:2334)

[28]
-, Classical Banach spaces, II: function spaces, Ergeb. Math. Grenzgeb., vol. 92, Springer-Verlag, New York, 1979. MR 540367 (81c:46001)

[29]
R. Mauldin (editor), The Scottish book; mathematics from the Scottish Café, Birkhäuser, Boston, MA, 1981. MR 666400 (84m:00015)

[30]
B. Maurey and G. Pisier, Séries de variables aléatoires vectorièlles independantes et priopriétés géométriques des espaces de Banach, Studia Math 58 (1976), 45-90. MR 0443015 (56:1388)

[31]
V. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Math., vol. 1200, Springer-Verlag, New York, 1986. MR 856576 (87m:46038)

[32]
E. Odell and T. Schlumprecht, The distortion problem, preprint. MR 1301394 (96a:46031)

[33]
A. Pelczynski, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228. MR 0126145 (23:A3441)

[34]
H. P. Rosenthal, A characterization of Banach spaces containing $ {l_1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. MR 0358307 (50:10773)

[35]
-, On subspaces of $ {L^p}$, Ann. of Math. (2) 97 (1973), 344-373. MR 0312222 (47:784)

[36]
-, Characterization of Banach spaces containing $ {c_0}$, preprint.

[37]
T. Schlumprecht, An arbitrarily distortable Banach space, preprint. MR 1177333 (93h:46023)

[38]
-, A complementary minimal Banach space not containing $ {c_0}$ or $ {l_p}$, preprint.

[39]
B. S. Tsirelson, Not every Banach space contains $ {l_p}$ or $ {c_0}$, Functional Anal. Appl. 8 (1974), 138-141.


Additional Information:

Reviewer(s):
Peter G. Casazza

Review Information:
Journal: Bull. Amer. Math. Soc. 30 (1994), 117-124.
DOI: 10.1090/S0273-0979-1994-00444-6
PII: S 0273-0979(1994)00444-6




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