Related papers: The SOH Operator System

We consider nonsymmetric operads with two binary operations satisfying relations in arity 3; hence these operads are quadratic, and so we can investigate Koszul duality. We first consider operations which are nonassociative (not necessarily…

In this paper we consider the $f$-orthomorphisms and $f$-linear operators on the order dual of an $f$-algebra. In particular, when the $f$-algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms,…

In this paper we study Toeplitz and Ces\`aro-type operators on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions for these operators to be continuous or…

We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…

We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectral sequence, we introduce a version of the Boardman--Vogt…

Here we prove a Poincar\'e-Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.

In these notes, we define a new simplicial structure on a connected multiplicative operad and call it connected multiplicative simplicial operad (for short; simplicial operad). Next we introduce on this simplicial operad a brace algebra…

This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…

We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…

We study composition operators acting on the weighted Bergman spaces on the bidisc, i.e. $C_{\Phi}:A^2_{\beta}(\mathbb{D}^2)\to A^2_{\beta}(\mathbb{D}^2)$ where $\Phi$ is induced by rational inner functions (RIFs) or a RIF and a smooth…

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…

We present a systematic development of inductive limits in the categories of ordered *-vector spaces, Archimedean order unit spaces, matrix ordered spaces, operator systems and operator C*-systems. We show that the inductive limit…

In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting…

We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a…

We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.

The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some…

We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…

This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational chains on configuration spaces of points in the plane form…

A recent paper of A.~Connes and W.D.~van Suijlekom identifies the operator system of $n\times n$ Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than $n$. The present paper examines this…

We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable. This result, together with its symmetric monoidal closed structure with respect to the projective tensor product of…