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

Toka Diagana (2006)

Commentationes Mathematicae Universitatis Carolinae

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 .

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

Dodzi Attimu, Toka Diagana (2007)

Commentationes Mathematicae Universitatis Carolinae

The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space 𝔼 ω × 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 × 𝔼 ω , then ϕ is representable by a unique linear operator A whose adjoint operator A * exists.

Representation of multilinear operators on C(K, X) spaces.

Ignacio Villanueva (2002)

RACSAM

We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.

Representation of operators by kernels.

Peter Stollmann (1991)

Collectanea Mathematica

We prove that differences of order-continuous operators acting between function spaces can be represented with a pseudo-kernel, proved the underlying measure spaces satisfy certain (rather weak) conditions. To see that part of these conditions are necessary, we show that the strict localizability of a measure space can be characterized by the existence of a pseudo-kernel for a certain operator.

Représentations de semi-groupes de mesures sur un groupe localement compact

Michel Duflo (1978)

Annales de l'institut Fourier

Soit T une distribution dissipative sur un groupe de Lie G et soit π une représentation fortement continue de G dans un espace de Banach. Supposons T à support compact. Il y a deux façons évidentes de définir un opérateur fermé π ( T ) : une faible et une forte. Le résultat principal de cet article est que l’on obtient le même résultat et que π ( T ) engendre un semi-groupe fortement continu d’opérateurs.

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