Related papers: Dominated Uryson operators on lattice-normed space…
We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given…
Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
Let $p\in(0,1]$ and $W$ be an $A_p$-matrix weight, which in scalar case is exactly a Muckenhoupt $A_1$ weight. In this article, we introduce matrix-weighted Hardy spaces $H^p_W$ via the matrix-weighted grand non-tangential maximal function…
This paper concerns positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space to the Riesz completion. It extends the order continuous norms in pre-Riesz spaces to Riesz completions.…
The concept of operator residuation for bounded posets with unary operation was introduced by the first two authors. It turns out that in some cases when these operators are transformed into lattice terms and the poset ${\mathbf P}$ is…
A well-known theorem due to R. C. James states that a Banach space is reflexive if and only if every bounded linear functional attains its norm. In this note we study Banach lattices on which every (real-valued) lattice homomorphism attains…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
An affine vertex operator construction at arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is…
Here, we clarify the physical aspects between the discrete Weyl-Wigner (W-W) formalism, well developed in condensed matter physics, and the so-called 'precise Weyl-Wigner calculus for lattice models' recently appearing in the literature. We…
A theorem of N. Katz \cite{Ka} p.45, states that an irreducible differential operator $L$ over a suitable differential field $k$, which has an isotypical decomposition over the algebraic closure of $k$, is a tensor product $L=M\otimes_k N$…
We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…
We characterize the modular and norm inequalities for the Dunkl-Hausdorff operator defined on non-negative non-increasing functions in the framework of the weighted Orlicz spaces.
We consider the nonautonomous Ornstein-Uhlenbeck operator in some weighted spaces of continuous functions in $\R^N$. We prove sharp uniform estimates for the spatial derivatives of the associated evolution operator $\OU$, which we use to…
We introduce the notions of strong asymptotic uniform smoothness and convexity. We show that the injective tensor product of strongly asymptotically uniformly smooth spaces is asymptotically uniformly smooth. This applies in particular to…
An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…
This is a continuation of recent work on the general definition of pseudo-differential operators of type $1,1$, in H\"ormander's sense. Continuity in $L_p$-Sobolev spaces and H\"older--Zygmund spaces, and more generally in Besov and…
In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of…
In this paper we continue the study of compact-like operators in lattice normed spaces started recently by Aydin, Emelyanov, Erkur\c{s}un \"Ozcand and Marabeh. We show among others, that every p-compact operator between lattice normed…
In this paper, we give Poisson and Cauchy representation theorems in Hardy-Orlicz spaces on the upper complex half-plane. We use these theorems for the construction of dual spaces of certain Hardy-Orlicz spaces and also for the…