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

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]**A. Borzyszkowski,*Unconditional decompositions and local unconditional structures in some subspaces of*, 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**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**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)**

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

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

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1191870-8

Article copyright:
© Copyright 1994
American Mathematical Society