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On Tsirelson’s space

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Abstract

A structure theory is developed for Tsirelson’s example of a Banach space which contains no isomorphic copy ofl p orc 0. In particular, it is shown that this space is the first example, other than subspaces ofl p andc 0, of a Banach space which embeds isomorphically into each of its infinite dimensional subspaces.

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Authors and Affiliations

  1. The University of Missouri, Missouri, USA

    P. G. Casazza, W. B. Johnson & L. Tzafriri

  2. The University of Alabama, Alabama, USA

    P. G. Casazza, W. B. Johnson & L. Tzafriri

  3. The Ohio State University, Ohio, USA

    P. G. Casazza, W. B. Johnson & L. Tzafriri

  4. Texas A&M University, Texas, USA

    P. G. Casazza, W. B. Johnson & L. Tzafriri

  5. The Hebrew University of Jerusalem, Jerusalem, Israel

    P. G. Casazza, W. B. Johnson & L. Tzafriri

  6. The University of Cambridge, Cambridge, UK

    P. G. Casazza, W. B. Johnson & L. Tzafriri

Authors
  1. P. G. Casazza
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  2. W. B. Johnson
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  3. L. Tzafriri
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Additional information

Supported in part by NSF MCS-8002221 and MCS-8102238.

Supported in part by NSF MCS-7903042.

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Casazza, P.G., Johnson, W.B. & Tzafriri, L. On Tsirelson’s space. Israel J. Math. 47, 81–98 (1984). https://doi.org/10.1007/BF02760508

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  • DOI: https://doi.org/10.1007/BF02760508

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