Chapter 38 Uniqueness of structure in banach spaces

Handbook of the Geometry of Banach Spaces

Volumn 2, Issue , 2003, Pages 1635-1669

  Tzafriri, Lior ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

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EID: 41549156141     PISSN: 18745849     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5849(03)80045-1     Document Type: Chapter

References (58)

1. p [0, 1]. Mat. Zametki 18 (1975) 313-325
2. (Russian). Babenko K.I. On conjugate functions. Dokl. Akad. Nauk SSSR 62 (1948) 157-160
3. Bernstein A.J. Maximally connected arrays on the n-cube. Discrete Math. 15 (1967) 1485-1489
4. 1-spaces in one and several variables. J. Funct. Anal. 46 (1982) 45-47
5. 1-spaces in a different number of variables. Bull. Soc. Math. Belg. Sér. B 35 (1983) 127-136
6. Bourgain J., Casazza P.G., Lindenstrauss J., and Tzafriri L. Banach Spaces with a Unique Unconditional Basis, up to Permutation. Mem. Amer. Math. Soc. 322 (1985)
7. Boyd D.B. Indices of function spaces and their relationship to interpolation. Canad. J. Math. 21 (1969) 1245-1254
8. Burkholder D.L. Martingales and singular integrals in Banach spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 1 (2001), Elsevier, Amsterdam 233-269
9. Casazza P.G., and Kalton N.J. Uniqueness of unconditional basis in Banach spaces. Israel J. Math. 103 (1998) 141-176
10. 0 products, Preprint.
11. Casazza P.G., Kalton N.J., and Tzafriri L. Uniqueness of unconditional and symmetric structions infinite dimensional spaces. Illinois J. Math. 34 (1990) 793-836
12. P.G. Casazza and M.C. Lammers, Genus N Banach spaces, Preprint.
13. Davis W.J. Embedding spaces with unconditional bases. Israel J. Math. 20 (1975) 189-191
14. p onto subspaces spanned by independent random variables. Compositio Math. 39 (1979) 141-175
15. Dragilev M.M. Canonical forms of a basis in the space of analytic function spaces. Uspekhi Mat. Nauk 15 (1960) 181-188
16. (Russian). Dragilev M.M. On regular bases in nuclear spaces. Mat. Sbornik 68 (1965) 153-173
17. Dragilev M.M. Topological vector spaces with equivalent bases. Mat. Zametki 28 (1980) 947-951
18. Dubinsky E. The Structure of Nuclear Fréchet Spaces. Lecture Notes in Math. 720 (1979), Springer
19. Edelstein I.S., and Wojtaszczyk P. On projections and unconditional bases in direct sums of Banach spaces. Studia Math. 56 (1976) 263-276
20. Figiel T., and Johnson W.B. A uniformly convex Banach space which contains no tp. Compositio Math. 29 (1974) 179-190
21. Figiel T., and Wojtaszczyk P. Special bases in functional spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 1 (2001), Elsevier, Amsterdam 561-597
22. Garnett J. Bounded Analytic Functions (1981), Academic Press, Orlando
23. Gowers W.T. A finite-dimensional Banach space with two non-equivalent symmetric bases. Israel J. Math. 87 (1994) 143-151
24. Harper L.H. Optimal assignments to number of vertices. SIAM J. Appl. Math. 12 (1964) 131-135
25. Hart S. A note on the edges of the n-cube. Discrete Math. 14 (1976) 157-163
26. Hernandez F., and Kalton N.J. Subspaces of rearrangement invariant spaces. Canad. J. Math. 48 (1996) 794-833
27. Johnson W.B., Maurey B., Schechtman G., and Tzafriri L. Symmetric Structures in Banach Spaces. Mem. Amer. Math. Soc. 217 (1979)
28. Kalton N.J. Orlicz sequence spaces without local convexity. Math. Proc. Cambridge Philos. Soc. 81 (1977) 253-278
29. Kalton N.J. Lattice Structures on Banach Spaces. Mem. Amer. Math. Soc. 493 (1993)
30. Kalton N.J., Leranoz C., and Wojtaszczyk P. Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces. Israel J. Math. 72 (1990) 299-311
31. Kalton N.J., Peck N.T., and Roberts J.W. An F-space Sample. London Math. Soc. Lecture Notes Ser. 89 (1984), Cambridge Univ. Press
32. Käthe G., and Täplitz O. Theorie der halbfiniten unendlichen Matrizen. J. Reine Angew. Math. 165 (1931) 116-127
33. p), 0 < p < 1. Studia Math. 102 (1992) 193-207
34. Lindenstrauss J. A remark on symmetric bases. Israel J. Math. 13 (1972) 317-320
35. p spaces and their applications. Studia Math. 29 (1968) 275-326
36. Lindenstrauss J., and Tzafriri L. On Orlicz sequence spaces III. Israel J. Math. 14 (1973) 368-389
37. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces I, Sequence Spaces (1977), Springer, Berlin
38. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces II, Function Spaces (1979), Springer, Berlin
39. Lindenstrauss J., and Zippin M. Banach spaces with a unique unconditional basis. J. Funct. Anal. 3 (1969) 115-125
40. Lindsey J.H. Assignments of numbers to vertices. Amer. Math. Monthly 71 (1964) 508-516
41. p. Asterisque 11 (1974)
42. McCarthy C.A., and Schwartz J. On the norm of a finite Boolean algebra of projections and applications to theorems of Kreis s and Morton. Comm. Pure Appl. Math. 18 (1965) 191-201
43. Mityagin B.S. Nuclear Riesz scales. Dokl. Akad. Nauk SSSR 137 (1961) 519-522
44. (Russian). Mityagin B.S. Approximative dimension and bases in nuclear spaces. Uspekhi Mat. Nauk 16 (1961) 63-132
45. Nawrocki M., and Ortynski A. The Mackey topology and complemented subspaces of Lorentz sequence spaces d (w, p) for 0 < p < 1. Trans. Amer. Math. Soc. 287 (1985) 713-722
46. Paley R.E. A remarkable series of orthogonal functions. Proc. London Math. Soc. 34 (1932) 241-264
47. Pelczynski A. Universal bases. Studia Math. 32 (1969) 247-268
48. p-spaces. Studia Math. 52 (1975) 263-289
49. Pelczynski A., and Singer I. On non-equivalent bases and conditional bases in Banach spaces. Studia Math. 25 (1964) 5-25
50. Read C.J. A Banach space with up to equivalence, precisely two symmetric bases. Israel J. Math. 40 (1981) 33-53
51. p (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 (1970) 273-303
52. Schechtman G. On Pelczynski's paper, "Universal bases". Israel J. Math. 22 (1975) 181-184
53. Schütt C. On the uniqueness of symmetric bases in finite-dimensional Banach spaces. Israel J. Math. 40 (1981) 97-117
54. 0. Functional Anal. Appl. 8 (1974) 138-141
55. p-spaces p≤1, and spline systems. Studia Math. 77 (1984) 289-320
56. Wojtaszczyk P. Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces II. Israel J. Math. 97 (1997) 253-280
57. Zahariuta V.P. On Isomorphic Classification of F-spaces. Lecture Notes in Math. 1043 (1983), Springer
58. Zippin M. On perfectly homogeneous bases in Banach spaces. Israel J. Math. 4 (1966) 265-272