Related papers: The Shilov boundary for a local operator system

We show that the Shilov boundary ideal for a separable Fr\'{e}chet local operator system is given by the intersection of the kernels of all its $\Gamma$-boundary representations.

To extend the notion of the injective envelope of a unital operator space to the locally convex case, Dosi (2014) first introduced the notion of the injective R-envelope for a unital operator space and then defined the injective R-envelope…

This is a companion to recent papers of the authors; here we construct the `noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the…

We describe the Shilov boundary ideal for a q-analog of algebra of holomorphic functions on the unit ball in the space of $2\times 2$ matrices.

In this paper, we analyze an optimization problem for the first (nonlinear) Steklov eigenvalue plus a boundary potential with respect to the potential function which is assumed to be uniformly bounded and with fixed $L^1$-norm.

We use layer potential to establish that the boundary biharmonic Steklov operators are elliptic pseudo-differential operators. Thus we are able to establish lower bounds on both the measure of boundary nodal sets and interior nodal sets for…

We generalize some facts about function algebras to operator algebras, using the `noncommutative Shilov boundary' or $C^*$-envelope first considered by Arveson. In the first part we study and characterize complete isometries between…

We prove optimal H\"older boundary regularity for a non-local operator with a singular, symmetric kernel that depends on the distance to the boundary of the underlying domain. Additionally, we prove higher boundary regularity of solutions.

We present a survey of past research activities and current results in constructing a mathematical framework describing the principle of local reflexivity for operator ideals and reveal further applications involving operator ideal products…

We study operator spaces, operator algebras, and operator modules, from the point of view of the `noncommutative Shilov boundary'. In this attempt to utilize some `noncommutative Choquet theory', we find that Hilbert C$^*-$modules and their…

We introduce a notion of the Bergman-Shilov (or Shilov) boundary for some subclasses of upper-semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of…

This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…

In this paper, we study the local spectral properties for both unilateral and bilateral weighted shift operators.

In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work done by Godefroy and Kalton and give some partial answers on the equivalence between the bounded…

A learning approach for determining which operator from a class of nonlocal operators is optimal for the regularization of an inverse problem is investigated. The considered class of nonlocal operators is motivated by the use of squared…

We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.

The concept of a local infimum for an optimal control problem is introduced. This definition extends that of an optimal process. For a~local infimum we prove an existence theorem and derive necessary conditions that resemble some family of…

We consider a class of quasilinear operators on a bounded domain $\Omega\subset \mathbb R^n$ and address the question of optimizing the first eigenvalue with respect to the boundary conditions, which are of the Robin-type. We describe the…

In this work we show endpoint boundedness properties of pseudo-differential operators of type $(\rho,\rho)$, $0<\rho<1$, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols.

We consider the Schrodinger operator a given domain. Our goal is to study some optimization problems where an optimal (non-negative) potential V has to be determined in some suitable admissible classes and for some suitable optimization…