Uniqueness of unconditional bases in Banach spaces
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We prove a general results on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique unconditional basis.
KeywordsSequence Space Banach Lattice Canonical Basis Unconditional Basis Orlicz Function
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- B. Bollobas,Combinatorics, Cambridge University Press, 1986.Google Scholar
- J. Bourgain, P. G. Casazza, J. Lindenstrauss and L. Tzafriri,Banach spaces with a unique unconditional basis, up to a permutation, Memoirs of the American Mathematical Society No. 322, 1985.Google Scholar
- J. Bourgain, N. J. Kalton and L. Tzafriri,Geometry of finite-dimensional subspaces and quotients of L p, Lecture Notes in Mathematics1376, Springer-Verlag, Berlin, 1989, pp. 138–175.Google Scholar
- W. T. Gowers and B. Maurey,Banach spaces with small spaces of operators, preprint.Google Scholar
- F. L. Hernandez and N. J. Kalton,Subspaces of rearrangement-invariant spaces, to appear.Google Scholar
- W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri,Symmetric structures in Banach spaces, Memoirs of the American Mathematical Society No. 217, 1979.Google Scholar
- N. J. Kalton,Lattice structures on Banach spaces, Memoirs of the American Mathematical Society No. 493, 1993.Google Scholar
- J. Lindenstrauss and A. Pełczynski,Absolutely summing operators in L p-spaces and their applications, Studia Mathematica29 (1968), 315–349.Google Scholar
- G. Pisier,The volume of convex bodies and geometry of Banach spaces, Cambridge Tracts 94, Cambridge University Press, 1989.Google Scholar