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Uniqueness of unconditional bases in Banach spaces

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

    P. G. Casazza & N. J. Kalton

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  1. P. G. Casazza
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  2. N. J. Kalton
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Correspondence to P. G. Casazza.

Additional information

Both authors were supported by NSF Grant DMS-9201357.

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Casazza, P.G., Kalton, N.J. Uniqueness of unconditional bases in Banach spaces. Isr. J. Math. 103, 141–175 (1998). https://doi.org/10.1007/BF02762272

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