Limit semigroups of Bernstein-Schnabl operators associated with positive projections
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
By using the concepts of limited -converging operators between two Banach spaces and , -sets and -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as -Dunford–Pettis property of order and Pelczyński’s property of order , .
If the minimum problem () is the limit, in a variational sense, of a sequence of minimum problems with obstacles of the type then () can be written in the form without any additional constraint.
Supposing that the metric space in question supports a fractional diffusion, we prove that after introducing an appropriate multiplicative factor, the Gagliardo seminorms of a function f ∈ L²(E,μ) have the property , where ℰ is the Dirichlet form relative to the fractional diffusion.
We collect and extend results on the limit of as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and is the intrinsic seminorm of order l+σ in the Sobolev space . In general, the above limit is equal to , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation of the methods by means of the corresponding dual functional. Finally, some examples of limiting function spaces are given.
The estimate is shown to hold if and only if is elliptic and canceling. Here is a homogeneous linear differential operator of order on from a vector space to a vector space . The operator is defined to be canceling if . This result implies in particular the classical Gagliardo–Nirenberg–Sobolev inequality, the Korn–Sobolev inequality and Hodge–Sobolev estimates for differential forms due to J. Bourgain and H. Brezis. In the proof, the class of cocanceling homogeneous linear differential...
We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
It is proved that if X is infinite-dimensional, then there exists an infinite-dimensional space of X-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that , the measures with non-σ-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl....
This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the...