More lr saturated L∞ spaces
2000 Mathematics Subject Classification: 05D10, 46B03.Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.
2000 Mathematics Subject Classification: 05D10, 46B03.Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.
In this article we formalize the definition and some facts about continuous functions from R into normed linear spaces [14].
We show that the stable C*-algebra and the related Ruelle algebra defined by I. Putnam from the irreducible Smale space associated with a topologically mixing expanding map of a compact metric space are strongly Morita equivalent to the groupoid C*-algebras defined directly from the expanding map by C. Anantharaman-Delaroche and V. Deaconu. As an application, we calculate the K⁎-group of the Ruelle algebra for a solenoid.
In a recent article, Kenny De Commer investigated Morita equivalence between locally compact quantum groups, in which a measured quantum groupoid, of basis ℂ², was constructed as a linking object. Here, we generalize all these constructions and concepts to the level of measured quantum groupoids. As for locally compact quantum groups, we apply this construction to the deformation of a measured quantum groupoid by a 2-cocycle.
In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences.
It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces , , to Lebesgue spaces . These conditions are expressed in terms of L²-based Sobolev spaces with sharp indices within the classes of multipliers we consider. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky (1977) and in the bilinear case (m = 2) by Miyachi and Tomita (2013). We also prove a coordinate-type Hörmander integral condition...