Abstract
We are concerned with some unbounded linear operators on the so-called p-adic Hilbert space E w . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on E w , and the solvability of the equation Au = v where A is a linear operator on E w .
Highlights
The primary goal of this paper is to investigate upon some unbounded linear operators on the so-called p-adic Hilbert space E ω
Afterwards, it goes back to introduce an unitary operator Γ on E ω × E ω which yields a remarkable description of A∗, the adjoint of a linear operator A defined on E ω which does have an adjoint, in terms of A
Let us mention that the p-adic Hilbert space E ω will play a key role throughout the paper
Summary
Towards a theory of some unbounded linear operators on p-adic Hilbert spaces and applications. (http://ambp.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://ambp.cedram.org/legal/). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Publication éditée par le laboratoire de mathématiques de l’université Blaise-Pascal, UMR 6620 du CNRS. Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/
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