On constructing Banach spaces with no unconditional basis

Komorowski, Ryszard

doi:10.1090/S0002-9939-1994-1191870-8

On constructing Banach spaces with no unconditional basis

Author: Ryszard Komorowski
Journal: Proc. Amer. Math. Soc. 120 (1994), 101-107
MSC: Primary 46B15; Secondary 46B70
DOI: https://doi.org/10.1090/S0002-9939-1994-1191870-8
MathSciNet review: 1191870
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: There exists a weak Hilbert space with no unconditional basis.

[BL] J. Bergh and J. Löfström, Interpolation spaces, Springer-Verlag, Berlin, 1976.
[B] Andrzej Borzyszkowski, Unconditional decompositions and local unconditional structures in some subspaces of 𝐿_{𝑝}, 1≤𝑝<2, Studia Math. 76 (1983), no. 3, 267–278. MR 729107
[CS] P. Casazza and T. Shura, Tsirelson's space, Lecture Notes in Math., vol. 1363, Springer-Verlag, New York, 1963.
[JLS] W. B. Johnson, J. Lindenstrauss, and G. Schechtman, On the relation between several notions of unconditional structure, Israel J. Math. 37 (1980), no. 1-2, 120–129. MR 599307, https://doi.org/10.1007/BF02762873
[JP] W. B. Johnson and G. Pisier, The proportional UAP characterizes weak Hilbert spaces, J. London Math. Soc. (2) 44 (1991), no. 3, 525–536. MR 1149013, https://doi.org/10.1112/jlms/s2-44.3.525
[KP] N. J. Kalton and N. T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1–30. MR 542869, https://doi.org/10.1090/S0002-9947-1979-0542869-X
[K] Timo Ketonen, On unconditionality in 𝐿_{𝑝} spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 35 (1981), 42. MR 612350
[NT] N. J. Nielsen and N. Tomczak-Jaegermann, Banach lattices with property (H) and weak Hilbert spaces, Illinois J. Math. 36 (1992), no. 3, 345–371. MR 1161972
[P] G. Pisier, Volume of convex bodies and the geometry of Banach spaces, Cambridge Univ. Press, Cambridge, 1990.
[TJ] Nicole Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 993774