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)

 
 

 

A Fréchet-Schwartz space with basis having a complemented subspace without basis


Author: Jari Taskinen
Journal: Proc. Amer. Math. Soc. 113 (1991), 151-155
MSC: Primary 46A35; Secondary 46A04, 46A11
DOI: https://doi.org/10.1090/S0002-9939-1991-1049851-8
MathSciNet review: 1049851
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using a method introduced by Pelczyński we show that for a nuclear Fréchet space $ E$ without basis we can find a Fréchet-Schwartz space $ F$ with basis containing a complemented, isomorphic copy of $ E$.


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

  • [D1] E. Dubinsky, The structure of nuclear Fréchet spaces, Lecture Notes in Math., vol. 720, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR 537039 (81f:46004)
  • [D2] -, Bases in complemented subspaces of power series spaces, Bull. Acad. Polon. Sci. 34 (1986), 65-67. MR 850315 (87h:46021)
  • [F] U. Fachinger, Diplomarbeit, Wuppertal, 1985.
  • [J] H. Jarchow, Locally convex spaces, Teubner, Stuttgart, 1981. MR 632257 (83h:46008)
  • [K] J. Krone, Existence of bases and the dual splitting relation for Fréchet spaces, preprint. MR 984848 (90c:46008)
  • [M1] B. Mityagin, Sur l'equivalence des bases inconditionelles dans les echelles de Hilbert, C.R. Acad. Sci. Paris 269 (1969), 426-428.
  • [M2] -, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970/71), 111-137. MR 0322470 (48:832)
  • [M3] B. Mityagin and G. Henkin, Linear problems in complex analysis, Uspekhi Mat. Nauk 26 (1971), 93-152. MR 0287297 (44:4504)
  • [P] A. Pelczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-243. MR 0308753 (46:7867)
  • [S] S. Szarek, A Banach space without a basis which has the bounded approximation property, Acta Math. 159 (1987), 81-98. MR 906526 (88f:46029)
  • [V] D. Vogt, Tame spaces and power series spaces, Math. Z. 196 (1987), 523-536. MR 917235 (89i:46005)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A35, 46A04, 46A11

Retrieve articles in all journals with MSC: 46A35, 46A04, 46A11


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1049851-8
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society