Some versions of Anderson's and Maher's inequalities. I.
The main object of this paper is to introduce and study some sequence spaces which arise from the notation of generalized de la Vallée–Poussin means and the concept of a modulus function.
Let T be a continuous linear operator acting on a Banach space X. We examine whether certain fundamental results for hypercyclic operators are still valid in the Cesàro hypercyclicity setting. In particular, in connection with the somewhere dense orbit theorem of Bourdon and Feldman, we show that if for some vector x ∈ X the set Tx,T²/2 x,T³/3 x, ... is somewhere dense then for every 0 < ε < 1 the set (0,ε)Tx,T²/2 x,T³/3 x,... is dense in X. Inspired by a result of Feldman, we also prove...
∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone...
Theory of -invariant linear operators which was considered for a group of congruences [2], [3] is now extended to a group of homeomorphisms. An analysis is carried out in order to establish to what extent the main results of the previous theory still hold under the actual very general assumptions.
Nous étudions les sous-espaces biinvariants du shift usuel sur les espaces à poidsoù et , pour un certain entier . Nous montrons que la trace analytique de tout sous-espace biinvariant est de type spectral, lorsque diverge, mais que ceci n’est plus valable lorsque converge.
We improve a result of Charpentier [Studia Math. 198 (2010)]. We prove that even on Fréchet spaces with a continuous norm, the existence of only one restrictively universal series implies the existence of a closed infinite-dimensional subspace of restrictively universal series.
T. Trent gave a new characterization of subnormality for an operator on a Hilbert space. T. Bînzar and D. Păunescu generalized this condition to commuting triples of operators. Here, we give an n-variable unbounded version of the above results. Theorems of this kind have also been obtained by Z. J. Jabłoński and J. Stochel.