On a generalization of the Corona problem.
On a generalization of W*-modules
a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.
On a generalized -inner product and the corresponding Cauchy-Schwarz inequality.
On a higher-order Hardy inequality
The Hardy inequality with holds for if is an open set with a sufficiently smooth boundary and if . P. Hajlasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for .
On -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On a lattice characterization of Hilbert spaces
On a limit at infinity notion of an ultradistribution. (Sur une notion de limite à l'infini d'une ultradistribution.)
On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.
On a Marinescu Structure on ... (X)
On a Method of Moments
On a necessary condition in the calculus of variations in Orlicz-Sobolev spaces
On a necessary condition in the calculus of variations in Sobolev spaces with variable exponent
We prove an approximation theorem in generalized Sobolev spaces with variable exponent and we give an application of this approximation result to a necessary condition in the calculus of variations.
On a new method in intuitionist linear analysis
On a New Segal Algebra.
On a nonlinear compactness lemma in .
On a nonlinear Peetre's theorem in full Colombeau algebras
We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras.
On a pair of automorphisms of -algebras
On a Problem of Bellenot and Dubinsky.
On a problem of Bertram Yood
In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.
On a problem of commutativity of automorphisms.