On the Algebraic Dimension Of Banach Spaces Over Non-Archimedean Valued Fields Of Arbitrary Rank

Herminia Ochsenius, W. H. Schikhof

Resumen


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).

Palabras clave


Banach spaces ; Valued fields ; Algebraic dimension.

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Referencias


T. Jech. Set Theory. San Diego: Academic Press. U. S. A., (1978).

G. Köthe. Topological Vector spaces. New York: Springer-Verlag, (1969).

H. Ochsenius and W. Schikhof. Banach spaces over fields with an in- finite rank valuation. In: p-adic Functional Analysis, Lecture Notes in pure and applied mathematics 207, edited by J. Kakol, N. De GrandeDe Kimpe and C. Perez-Garcia. Marcel Dekker, pp. 233-293, (1999).




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

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