This is a preview of subscription content, log in via an institution to check access.
References
I. Ameniya undY. Kōomura, Über nicht-vollständige Montelräume. Math. Ann.177, 273–277 (1968).
S.Banach, Théorie des opérations linéaires. New York 1978.
S. Bennet andJ. B. Cooper, Weak basis inF and (LF)-spaces. J. London Math. Soc.44, 505–508 (1969).
G. Bessaga andA. Pełczynski, Properties of bases in spaces of typeB 0. Prace Mat.3, 123–142 (1959).
M. De Wilde, Reseaux dans les espaces linéaires a semi-normes. Mem. Soc. R. Liège.18, 2 (1969).
M. De Wilde, On the equivalence of weak and Schauder basis. Proc. Int. Coll. on Nuclear Spaces and Ideals in Operator Algebras, Warsaw 1969, Studia Math.38, 457 (1970).
M.De Wilde, Closed graph theorems and webbed spaces. London-San Francisco-Melbourne 1978.
M. De Wilde andG. Houet, On increasing sequences of absolutely convex sets in locally convex spaces. Math. Ann.192, 257–261 (1971).
T. A. Efimova, On weak basis in the inductive limits of barrelled normed spaces. Vestnik Leningrad Uni. Math. Meb. Astronom.119, 21–26 (1981).
K. Floret, Bases in sequentially retractive limits spaces. Proc. Int. Coll. on Nuclear Spaces and Ideals in Operators Algebras, Warsaw 1969, Studia Math.38, 221–226 (1970).
H.Jarchow, Locally convex spaces. Stuttgart 1981.
G.Köthe, Topological vector spaces I and II. Berlin-Heidelberg-New York 1969–1979.
C. W. McArthur, The weak basis theorem. Coll. Math.17, 71–76 (1967).
C. W. McArthur, Developements in Schauder basis theory. Bull. Amer. Math. Soc. (6)78, 877–907 (1972).
W. F. Newns, On the representation of analytic functions by infinite series. Phil. Trans. Roy. Soc. London (A)245, 429–468 (1953).
S. Saxon, Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology. Math. Ann.197, 87–106 (1972).
M. Valdivia, Absolutely convex sets in barrelled spaces. Ann. Inst. Fourier Grenoble,21, 3–13 (1971).
M.Valdivia, On suprabarrelled spaces. Functional Analysis, Holomorphy and Approximation Theory. Proceedings, Rio de Janeiro. LNM843, Berlin-Heidelberg-New York 1978.
M.Valdivia, Topics in locally convex spaces. Math. Stud.67, Amsterdam-New York-Oxford 1982.
M.Valdivia, Barrelled spaces related with the closed graph theorem. To be published in Port. Math. 1984.
M. Valdivia andP. Perez-Carreras, On totally barrelled spaces. Math. Z.178, 263–269 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Orihuela, J. On the equivalence of weak and Schauder bases. Arch. Math 46, 447–452 (1986). https://doi.org/10.1007/BF01210785
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01210785