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

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

Toka Diagana (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 φ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then φ is representable by a unique self-adjoint (possibly unbounded) operator A .

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 ⊗ Y in non-archimedean Hilbert space, where D λ is a diagonal operator and X ⊗ 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.