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Banach spaces with a unique unconditional basis, up to permutation

About this Title

J. Bourgain, P. G. Casazza, J. Lindenstrauss and L. Tzafriri

Publication: Memoirs of the American Mathematical Society
Publication Year 1985: Volume 54, Number 322
ISBNs: 978-0-8218-2323-1 (print); 978-1-4704-0735-3 (online)
MathSciNet review: 782647
MSC: Primary 46B15

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Table of Contents


  • 0. Introduction
  • 1. Unconditional bases of finite direct sums of Banach spaces
  • 2. Infinite direct sums of Hilbert spaces
  • 3. Infinite direct sums of $\ell _1$-spaces in the sense of $c_0$, Part I
  • 4. Infinite direct sums of $\ell _1$-spaces in the sense of $c_0$, Part II
  • 5. Infinite direct sums in the sense of $\ell _2$
  • 6. Prime spaces
  • 7. Tsirelson’s space
  • 8. Complemented subspaces of $(\sum ^\infty _{n=1} \oplus \ell ^n_2)_1$ and $(\sum ^\infty _{n=1} \oplus \ell ^n_\infty )_1$
  • 9. “Large” subspaces of $(\ell _q \oplus \ell _q \oplus \cdots \oplus \ell _q \oplus \cdots )_p$
  • 10. Complemented subspaces of $(\ell _2 \oplus \ell _2 \oplus \cdots \oplus \ell _2 \oplus \cdots )_1$ and $(c_0 \oplus c_0 \oplus \cdots \oplus c_0 \oplus \cdots )_1$
  • 11. Open problems
  • 12. References