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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.3 Antofagasta Dec. 2007

http://dx.doi.org/10.4067/S0716-09172007000300001 

 

Proyecciones Journal of Mathematics
Vol. 26, Nº 3, pp. 237-244, December 2007.
Universidad Católica del Norte
Antofagasta - Chile


ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK


HERMINIA OCHSENIUS 1
W. H. SCHIKHOF 2

1 Pontificia Universidad Católica de Chile, Chile.
2 Raboud University, The Netherlands.

Correspondencia a:



Abstract
Let K be a complete non-archimedean valued field of any rank, and let E be a K-Banach space with a countable topological base. We determine the algebraic dimension of E (2.3, 2.4, 3.1).


Key words : Banach spaces, valued fields, algebraic dimension.
AMS Classification [2000] : Primary 46S10.

REFERENCES
[1] T. Jech. Set Theory. San Diego: Academic Press. USA, (1978).
[2] G. Köthe. Topological Vector spaces. New York: Springer-Verlag, (1969).
[3] H. Ochsenius and W. Schikhof. Banach spaces over fields with an infinite rank valuation. In: p-adic Functional Analysis, Lecture Notes pure and applied mathematics 207, edited by J. Kakol, N. De Grande- De Kimpe and C. Perez-Garcia. Marcel Dekker, pp. 233-293, (1999).

HERMINIA OCHSENIUS
Facultad de Matemáticas
Pontificia Universidad Católica de Chile
Casilla 306 - Correo 22
Santiago
Chile
e-mail : mailto:hochsen@mat.puc.cl

W. H. SCHIKHOF
Department of Mathematics
Radboud University
Toernooiveld 6525 ED Nijmegen
The Netherlands
e-mail : mailto:w_schikhof@hetnet.nl

Received : July 2007. Accepted : October 2007

 

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