Related papers: Operator Theory on the Pentablock

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

This paper gives a concept of an integral operator defined on a manifold $M$ consisting of triple of points in $\mathbb{R}^{d}$ making up a regular $3$-simplex with the origin. The boundedness of such operator is investigated. The…

We consider a second-order differential equation $$ -y''(z)-(iz)^{N+2}y(z)=\lambda y(z), \quad z\in \Gamma $$ with an eigenvalue parameter $\lambda \in \mathbb{C}$. In $\mathcal{PT}$ quantum mechanics $z$ runs through a complex contour…

We characterize the essential spectrum of the plasmonic problem for polyhedra in $\mathbb{R}^3$. The description is particularly simple for convex polyhedra and permittivities $\epsilon < - 1$. The plasmonic problem is interpreted as a…

We find an explicit tetrablock isometric dilation for every member $(A_\alpha, B, P)$ of a family of tetrablock contractions indexed by a parameter $\alpha$ in the closed unit disc (only the first operator of the tetrablock contraction…

We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…

We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…

We consider a set of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS${}_5 \times S^5$. These single-particle operators are defined to…

The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The…

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…

We introduce $p$-adic operator algebras, which are nonarchimedean analogues of $C^*$-algebras. We demonstrate that various classical examples of operator algebras - such as group(oid) $C^*$-algebras - have nonarchimedean counterparts. The…

For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…

In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-\Delta_g)^s)u := \sum_{i=1}^M \alpha_i(-\Delta_{g_i})^{s_i}u\] for $s=(s_1,\dots,s_M)$,…

We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…

We study the triplet vertex operator algebra $\mathcal{W}(p)$ of central charge $1-\frac{6(p-1)^2}{p}$, $p \geq 2$. We show that $\trip$ is $C_2$-cofinite but irrational since it admits indecomposable and logarithmic modules. Furthermore,…

In this article, we give an abstract characterization of the ``identity'' of an operator space $V$ by looking at a quantity $n_{cb}(V,u)$ which is defined in analogue to a well-known quantity in Banach space theory. More precisely, we show…

For a graph $G$, let $\mathscr{C}_5(G)$ denote the graph whose vertices are the induced $5$-cycles of $G$, where two vertices are adjacent whenever the corresponding cycles share an edge. We investigate the iterative behavior of the…

There are considered isometries on a Hilbert space. By the Wold theorem any isometry can be decomposed into a unitary operator and a unilateral shift. For a pair of isometries, even commuting, a maximal subspace reducing one isometry to a…

In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing…

Vertex operators in string theory come in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically…