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Topological dual of B ∞ ( I , ₁ ( X , Y ) ) with application to stochastic systems on Hilbert space

N.U. Ahmed (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...

Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications

Toka Diagana (2005)

Annales mathématiques Blaise Pascal

We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space 𝔼 ω . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on 𝔼 ω , and the solvability of the equation A u = v where A is a linear operator on 𝔼 ω .

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

Trace and determinant in Jordan-Banach algebras.

Bernard Aupetit, Abdelaziz Maouche (2002)

Publicacions Matemàtiques

Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the...

Trace formulae for p-hyponormal operators

Muneo Chō, Tadasi Huruya (2004)

Studia Mathematica

The purpose of this paper is to introduce mosaics and principal functions of p-hyponormal operators and give a trace formula. Also we introduce p-nearly normal operators and give trace formulae for them.

Transformation de Poisson sur un arbre localement fini

Ferdaous Kellil, Guy Rousseau (2005)

Annales mathématiques Blaise Pascal

Dans cet article on étudie en premier lieu la résolvante (le noyau de Green) d’un opérateur agissant sur un arbre localement fini. Ce noyau est supposé invariant par un groupe G d’automorphismes de l’arbre. On donne l’expression générique de cette résolvante et on établit des simplifications sous différentes hypothèses sur G .En second lieu on introduit la transformation de Poisson qui associe à une mesure additive finie sur l’espace Ω des bouts de l’arbre une fonction propre de l’ opérateur. On...

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