Remarks on Banach- -algebras. (Remarques sur les -algèbres de Banach.)
Remarks on bases in a Fréchet function space.
Remarks on bounded sets in -spaces
We establish the relationship between regularity of a Hausdorff -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff -space to be an -space. A factorization theorem for -spaces with property (K) is also obtained.
Remarks on Catalan and super-Catalan numbers
In this article we discuss the Catalan and super-Catalan (or Schröder) numbers. We start with some combinatorial interpretations of those numbers. We study two probability measures in the context of free probability, one whose moments are super-Catalan, and another, whose even moments are super-Catalan and odd moments are zero. With the use of the latter we also show some new formulae for evaluation of the Catalans in terms of super-Catalans and vice-versa.
Remarks on compact operators between interpolation spaces associated to polygons.
This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.
Remarks on conditional moments of the free deformed Poisson random variables
We will show that the conditional first moment of the free deformed Poisson random variables (q = 0) corresponding to operators fulfilling the free relation is a linear function of the regression and the conditional variance also is a linear function of the regression. For this purpose we will first demonstrate some properties of the Wick product and then we will concentrate on the free deformed Poisson random variables.
Remarks on continuous images of Radon-Nikodým compacta
A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact we prove: If is totally disconnected, then it is Radon-Nikod’ym compact. If is adequate, then it is even Eberlein compact.
Remarks on delta-convex functions
Remarks on embeddable semigroups in groups and a generalization of some Cuthbert's results.
Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions
We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on -almost everywhere Fréchet differentiability of Lipschitz functions on (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at -almost every at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are -almost everywhere Fréchet differentiable....
Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra
In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in , where denotes the Colombeau algebra.
Remarks on independent sequences and dimension in topological linear spaces.
Remarks on inequalities of Poincaré type
Remarks on integration by parts in infinite dimension
Remarks on interpolation of bilinear operators by methods associated to polygons
We study interpolation of bilinear operators by the polygons methods. We prove an interpolation theorem of type into spaces, and show the optimality of the precedings results.
Remarks on joint distributions of observables
Remarks on -spaces
Remarks on -subalgebras of
Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of containing...
Remarks on Nikodým's boundedness theorem.
Remarks on orthogonality preserving mappings in normed spaces and some stability problems.