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Applications of the p -adic Nevanlinna theory to functional equations

Abdelbaki Boutabaa, Alain Escassut (2000)

Annales de l'institut Fourier

Let K be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the p -adic Nevanlinna theory to functional equations of the form g = R f , where R K ( x ) , f , g are meromorphic functions in K , or in an “open disk”, g satisfying conditions on the order of its zeros and poles. In various cases we show that f and g must be constant when they are meromorphic in all K , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...

Biequivalence vector spaces in the alternative set theory

Miroslav Šmíd, Pavol Zlatoš (1991)

Commentationes Mathematicae Universitatis Carolinae

As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field Q of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...

C * -algebras of operators in non-archimedean Hilbert spaces

J. Antonio Alvarez (1992)

Commentationes Mathematicae Universitatis Carolinae

We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

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