Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

No infinite dimensional $ P$ space admits a Markuschevich basis


Author: William B. Johnson
Journal: Proc. Amer. Math. Soc. 26 (1970), 467-468
MSC: Primary 46.10
MathSciNet review: 0265916
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Theorem. Let $ X$ be a Banach space. If $ X$ is a Grothendieck space and $ X$ admits a Markuschevich basis then $ X$ is reflexive. This theorem is used to prove the conjecture of J. A. Dyer [1] stated in the title.


References [Enhancements On Off] (What's this?)

  • [1] J. A. Dyer, Generalized bases in $ P$-spaces (preprint).
  • [2] A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type 𝐶(𝐾), Canadian J. Math. 5 (1953), 129–173 (French). MR 0058866
  • [3] Joram Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. No. 48 (1964), 112. MR 0179580

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.10

Retrieve articles in all journals with MSC: 46.10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0265916-9
Keywords: Markuschevich basis, complete biorthogonal systems, $ P$ spaces, injective Banach spaces, Grothendieck spaces
Article copyright: © Copyright 1970 American Mathematical Society