相关论文: Lebesgue decompositions and the Gleason--Whitney p…
Bessel potential spaces have gained renewed interest due to their robust structural properties and applications in fractional partial differential equations (PDEs). These spaces, derived through complex interpolation between Lebesgue and…
The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient…
We introduce the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion: it is a simplicial infinity-groupoid satisfying an exactness condition weaker than the Segal condition, which expresses…
Let $X$ be a Borel and Borel-regular metric measure space whose closed balls are of positive and finite measure. In this paper, we shall give equivalent conditions for averaging operators on non-reflexive Lebesgue spaces $L^1(X)$ and…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
In the deBranges-Rovnyak functional model for contractions on Hilbert space, any completely non-coisometric (CNC) contraction is represented as the adjoint of the restriction of the backward shift to a deBranges-Rovnyak space, $\mathscr{H}…
As it is known, Gleason's theorem is not applicable for a two-dimensional Hilbert space since in this situation Gleason's axioms are not strong enough to imply Born's rule thus leaving room for a dispersion-free probability measure i.e.,…
We explain how Pusz--Woronowicz's idea of their functional calculus fits the theory of Lebesgue decomposition for positive operators on Hilbert spaces initially developed by Ando. In this way, we reconstruct the essential and fundamental…
Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_\omega$ to the Lebesgue space $L^q_\nu$, where $0<q<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights…
We consider compact group actions on C*- and W*- algebras. We prove results that relate the duality property of the action (as defined in the Introduction) with other relevant properties of the system such as the relative commutant of the…
We give in this short paper a sharp estimate for the norm of a multivariate dilation operator generated by multi-matrix (tensor) linear argument transformation (dilation operator) between two different weight Lebesgue-Riesz and Grand…
We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of $\mathbb{C}.$ In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not…
We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Cobos-Fern\'{a}ndez-Cabrera-Mart\'{i}nez theorem. Then, as an…
Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within the category of Lie algebras. We first show that no Lie…
We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…
In this paper we estimate the norm of operator acting from one Bilateral Grand Lebesgue Space (BGLS) into other Bilateral Grand Lebesgue Space. We also give some examples to show the sharpness of offered inequalities.
Let $0<\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\mathcal M}_\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we…
We introduce a so-called restricted, in particular, discrete version of (Banach) Grand Lebesgue Spaces (GLS), investigate its properties and derive the conditions of coincidence with the classical ones. We show also that these spaces forms…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…