Representation of bilinear forms in non-Archimedean Hilbert space by linear operators

Toka Diagana

Displaying similar documents to “Representation of bilinear forms in non-Archimedean Hilbert space by linear operators”

Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II

Dodzi Attimu, Toka Diagana (2007)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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

Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space

Toka Diagana, George D. McNeal (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The paper is concerned with the spectral analysis for the class of linear operators $A = D_{λ} + X \otimes Y$ in non-archimedean Hilbert space, where $D_{λ}$ 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.

$C^{*}$ -algebras of operators in non-archimedean Hilbert spaces

J. Antonio Alvarez (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

Displaying similar documents to “Representation of bilinear forms in non-Archimedean Hilbert space by linear operators”