Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 1191870
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

References [Enhancements On Off] (What's this?)

  • [BL] J. Bergh and J. Löfström, Interpolation spaces, Springer-Verlag, Berlin, 1976.
  • [B] A. Borzyszkowski, Unconditional decompositions and local unconditional structures in some subspaces of $ {L_p},\,1 \leqslant p < 2$, Studia Math. 76 (1983), 267-278. MR 729107 (86a:46015)
  • [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 notations of unconditional structure, Israel J. Math. 37 (1980), 120-129. MR 599307 (83f:46015)
  • [JP] W. B. Johnson and G. Pisier, The proportional U.A.P. characterizes weak Hilbert spaces, J. London Math. Soc. (2) 44 (1991), 525-536. MR 1149013 (93e:46019)
  • [KP] N. J. Kalton and T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30. MR 542869 (82g:46021)
  • [K] T. Ketonen, On unconditionality in $ {L_p}$ spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 35 (1983), 3-42. MR 612350 (82h:46020)
  • [NT] N. J. Nielsen and N. Tomczak-Jaegermann, Banach lattices with property $ (H)$ and weak Hilbert spaces, Illinois J. Math. (to appear). MR 1161972 (93i:46037)
  • [P] G. Pisier, Volume of convex bodies and the geometry of Banach spaces, Cambridge Univ. Press, Cambridge, 1990.
  • [TJ] N. Tomczak-Jaegermann, Banach-Mazur distance and finite-dimensional operator ideals, Pitman Monographs Surveys Pure Appl. Math., vol. 38, Longman Sci. Tech., Harlow, and Wiley, New York. MR 993774 (90k:46039)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B15, 46B70

Retrieve articles in all journals with MSC: 46B15, 46B70

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society