Abstract
In this note we show that the twisted Fréchet and (LB)-spaces constructed by the second author in [6, § 1] and which were known not to have unconditional bases may, however, have a basis.
Similar content being viewed by others
References
Floret, K., Moscatelli, V. B.: On bases in strict inductive and projective limits of locally convex spaces. Pacific J. Math.119, 103–113 (1985).
Floret, K., Moscatelli, V. B.: Unconditional bases in Fréchet spaces. Arch. Math.47, 129–130 (1986).
Jarchow, H.: Locally Convex Spaces. Stuttgart: Teubner. 1981.
Kadec, M. I., Pełczyński, A.: Bases, lacunary sequences and complemented subspaces in the spacesL p . Studia Math.21, 161–176 (1962).
Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Berlin-Heidelberg-New York: Springer. 1979.
Moscatelli, V. B.: Fréchet spaces without continuous norms and without bases. Bull. London Math. Soc.12, 63–66 (1980).
Singer, I.: Bases in Banach Spaces II. Berlin-Heidelberg-New York: Springer. 1981.
Author information
Authors and Affiliations
Additional information
This author acknowledges partial support from the Italian Ministero della Pubblica Istruzione.
Rights and permissions
About this article
Cite this article
Metafune, G., Moscatelli, V.B. A twisted Fréchet space with basis. Monatshefte für Mathematik 105, 127–129 (1988). https://doi.org/10.1007/BF01501165
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01501165