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Totally convex algebras

Dieter Pumplün, Helmut Röhrl (1992)

Commentationes Mathematicae Universitatis Carolinae

By definition a totally convex algebra A is a totally convex space | A | equipped with an associative multiplication, i.eȧ morphism μ : | A | | A | | A | of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces.

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 .

Towards a two-scale calculus

Augusto Visintin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf (2012)

Applicationes Mathematicae

We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem - d i v ( a ( x , u , u ) ) + g ( x , u ) = f - d i v F in Ω, where Ω is a bounded open domain of N , N ≥ 2 and a : Ω × × N N is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to i = 1 N L p ' ( · ) ( Ω ) .

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