### A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on ${c}_{0}$. For that, our first task consists of introducing a new class of linear operators denoted $W\left({c}_{0}(J,\omega ,\mathbb{K})\right)$ and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

The aim of this paper is the study of a certain class of compact-like sets within some spaces of continuous functions over non-Archimedean ground fields. As a result, some p-adic Ascoli theorems are obtained.

The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if $\phi $ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then $\phi $ is representable by a unique self-adjoint (possibly unbounded) operator $A$.

The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space ${\mathbb{E}}_{\omega}\times {\mathbb{E}}_{\omega}$ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi $ is a non-degenerate bilinear form on ${\mathbb{E}}_{\omega}\times {\mathbb{E}}_{\omega}$, then $\varphi $ is representable by a unique linear operator $A$ whose adjoint operator ${A}^{*}$ exists.

The paper is concerned with the spectral analysis for the class of linear operators $A={D}_{\lambda}+X\otimes Y$ in non-archimedean Hilbert space, where ${D}_{\lambda}$ is a diagonal operator and $X\otimes Y$ is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.