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On factors ofC([0, 1]) with non-separable dual

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An Erratum to this article was published on 01 March 1975

Abstract

LetC denote the Banach space of scalar-valued continuous functions defined on the closed unit interval. It is proved that ifX is a Banach space andT:C→X is a bounded linear operator withT * X * non-separable, then there is a subspaceY ofC, isometric toC, such thatT|Y is an isomorphism. An immediate consequence of this and a result of A. Pelczynski, is that every complemented subspace ofC with non-separable dual is isomorphic (linearly homeomorphic) toC.

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Authors and Affiliations

  1. University of California, Berkeley

    Haskell P. Rosenthal

Authors
  1. Haskell P. Rosenthal
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Additional information

The research for this paper was partially supported by NSF-GP-30798X.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02757135.

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Rosenthal, H.P. On factors ofC([0, 1]) with non-separable dual. Israel J. Math. 13, 361–378 (1972). https://doi.org/10.1007/BF02762811

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