By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

This quantity comprises papers according to lectures given on the 11th overseas convention on $p$-adic useful research, which used to be held from July 5-9, 2010, in Clermont-Ferrand, France. The articles gathered right here characteristic contemporary advancements in a variety of components of non-Archimedean research: Hilbert and Banach areas, finite dimensional areas, topological vector areas and operator thought, strict topologies, areas of constant features and of strictly differentiable services, isomorphisms among Banach capabilities areas, and degree and integration. different subject matters mentioned during this quantity comprise $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic services, the spectrum of a few algebras of analytic services, and maximal beliefs of the ultrametric corona algebra

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**Extra resources for Advances in non-Archimedean Analysis: 11th International Conference P-adic Functional Analysis July 5-9, 2010 Universite Blaise Pascal, Clermont-ferrand, France**

**Sample text**

When K is spherically complete), the p-Adic versions of these classical results remain true, and on the other hand, that there are examples showing that if those assumptions are removed then the results fail. In the last section of [67] a new “machine” to construct examples of inductive sequences was given. It was the source of most of the (counter)examples presented there, which either do not have a classical counterpart or if they do, still have a typically Archimedean character. A survey of the most important results of [65] and [67], together with the study of new variants of regularity as well as the relation between them, can be found in [68].

And the following conditions hold simultaneously: (1) b0 ≡ 1 (mod 2), b0 + b1 ≡ 3 (mod 4), b2 + b3 ≡ 2 (mod 4); (2) |bm |2 = 1 for m ≥ 2; 2n −1 (3) m=2n−1 bm ≡ 0 (mod 4) for n ≥ 3. 3 is the following lemma whose proof, in turn, uses results announced in [11] by the third of authors of the present paper. 4. 1). t. the measure μp ) if and only if the following conditions hold simultaneously: (1) B0 ≡ 1 (mod 2), B0 + B1 ≡ 3 (mod 4), (2) |Bm |2 = 2− log2 m , if m ≥ 2; (3) 2n −1 m=2n−1 (Bm − 2n−1 ) 2 ≤ 2−(n+1) , if n ≥ 2.

23 (1971), 123-166. [7] On spaces of operators between locally K-convex spaces. Indag. Math. 34 (1972), 113-129. [8] On the structure of locally K-convex spaces with a Schauder basis. Indag. Math. 34 (1972), 396-406. [9] On the Grothendieck approximation property in non-Archimedean Analysis. Nieuw Arch. Wisk. (3) 20 (1972), 242-245. [10] Sur une notion de pr´e-compacit´e utilisable dans la th´eorie des espaces localement “convexes” sur un corps topologique quelconque. C. R. Acad. Sci. Paris S´er.