The non-archimedean space
The non-archimedian space BC(X) with the strict topology.
Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.
The -adic -transform
The p-adic differential equation y' = wy in the closed unit disk.
The problems of the non-Archimedean analysis generated by quantum physics
The structure of ideals in the Banach algebra of Lipschitz functions over valued fields
The use of operators for the construction of normal bases for the space of continuous functions on .
The van der Put base for -functions.
The weak and strong convergence in metrizable spaces over valued fields.
Théorème de préparation différentiable ultramétrique, II
Topological vector spaces over topological division rings: barrelled, bornological and quasibarrelled spaces
Towards a theory of some unbounded linear operators on -adic Hilbert spaces and applications
We are concerned with some unbounded linear operators on the so-called -adic Hilbert space . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on , and the solvability of the equation where is a linear operator on .
Tree structure on the set of multiplicative semi-norms of Krasner algebras H(D).
Let K be an algebraically closed field, complete for an ultra- metric absolute value, let D be an infinite subset of K and let H(D) be the set of analytic elements on D. We denote by Mult(H(D), UD) the set of semi-norms Phi of the K-vector space H(D) which are continuous with respect to the topology of uniform convergence on D and which satisfy further Phi(f g)=Phi(f) Phi(g) whenever f,g elements of H(D) such that fg element of H(D). This set is provided with the topology of simple convergence....
Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space
Orthomodular spaces are the counterpart of Hilbert spaces for fields other than or . Both share numerous properties, foremost among them is the validity of the Projection theorem. Nevertheless in the study of bounded linear operators which started in [3], there appeared striking differences with the classical theory. In fact, in this paper we shall construct, on the canonical non-archimedean orthomodular space of [5], two infinite families of self-adjoint bounded linear operators having no...
Uma generalização não-arquimediana do teorema de Mahowald para espaços d-tonelados
Una nota sobre la extensión de formas lineales continuas de espacios normados no arquimedianos.
Una nota sobre las álgebras de Banach regulares no-arquimedianas.
Es bien conocido que el conjunto M de los ideales maximales de un álgebra de Banach compleja X es un espacio compacto y Hausdorff para la topología de Gelfand, y que X es isométricamente isomorfa al álgebra C(M,C) de las funciones continuas sobre M si y sólo si X es una B*-álgebra, es decir un álgebra de Banach con involución verificando ||x*x|| = ||x||2 (Gelfand-Naimark). En el caso no-arquimediano, X admite tal representación si y sólo si el subespacio vectorial engendrado por {e ∈ X | e2 = e,...
Valeurs absolues des algèbres de Krasner
Weak bases in -adic spaces
We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.
Weakly c'-compact subsets of non-archimedean Banach spaces over a spherically complete field.