2th International Conference on P-adic Functional Analysis Abstracts of Talks

José Aguayo (Universidad de Concepción, Chile) and Miguel Nova (Universidad Catolica de la Santisima, Chile) and Khodr Shamseddine (University of Manitoba, Canada) Title: Characterization of Compact and self-adjoint operators on Free Banach spaces of countable type over the complex Levi-Civita field Abstract: Let C be the complex Levi-Civita field and let E be a free Banach space over C of countable type. Since any such free Banach space is isometrically isomorphic to c0 (N, C, s) , where s : N → (0,∞) , it is enough to study c0 (N, C) [taking s to be the constant function 1], which will be denoted by c0(C) or, simply, c0. In this talk, we define a natural inner product on c0 which induces the sup-norm of c0. Of course, c0 is not orthomodular, so we characterize those closed subspaces of c0 with an orthonormal complement with respect to this inner product; that is, those closed subspaces M of c0 such that c0 = M ⊕M⊥. Such a subspace, together with its orthonormal complement, defines a special kind of projection, the so-called normal projection. We present a characterization of such normal projections as well as a characterization of another kind of operators, the compact operators on c0.