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Israel Journal of Mathematics

, Volume 7, Issue 4, pp 325–349 | Cite as

The ℒ p spaces

  • J. Lindenstrauss
  • H. P. Rosenthal
Article

Abstract

The ℒ p spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒ p space if and only ifX* is and ℒ q space (p −1+q −1=1). (ii) A complemented subspace of an ℒ p space is either an ℒ p or an ℒ2 space. (iii) The ℒ p spaces have sufficiently many Boolean algebras of projections. These results are applied to show thatX is an ℒ (resp. ℒ1) space if and only ifX admits extensions (resp. liftings) of compact operators havingX as a domain or range space. We also prove a theorem on the “local reflexivity” of an arbitrary Banach space.

Keywords

Banach Space Boolean Algebra Compact Operator Isomorphic Type Closed Linear Span 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Weizmann Science Press of Israel 1969

Authors and Affiliations

  • J. Lindenstrauss
    • 1
    • 2
  • H. P. Rosenthal
    • 1
    • 2
  1. 1.Hebrew University of JerusalemIsrael
  2. 2.University of CaliforniaBerkeley

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