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Tsirelson-like spaces and complexity of classes of Banach spaces

  • Ondřej Kurka
Original Paper
  • 88 Downloads

Abstract

Employing a construction of Tsirelson-like spaces due to Argyros and Deliyanni, we show that the class of all Banach spaces which are isomorphic to a subspace of \( c_{0} \) is a complete analytic set with respect to the Effros Borel structure of separable Banach spaces. Moreover, the classes of all separable spaces with the Schur property and of all separable spaces with the Dunford–Pettis property are \(\Pi ^{1}_{2} \)-complete.

Keywords

Effros Borel structure Complete analytic set Tsirelson space Banach space \( c_{0} \) Schur property 

Mathematics Subject Classification

Primary 46B25 54H05 Secondary 46B03 46B20 

Notes

Acknowledgements

The author is grateful to the referees for numerous suggestions that helped to improve the manuscript.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of Mathematical Analysis, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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