Related papers: Two commuting operators associated with a tridiago…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
We represent and classify pairs of commuting isometries $(V_1, V_2)$ acting on Hilbert spaces that satisfy the condition \[ [V_1^*, V_2] = \text{compact and normal}, \] where $[V_1^*, V_2] := V_1^* V_2 - V_2 V_1^*$ is the cross-commutator…
We establish a relationship between Schreiner's matrix regular operator space and Werner's (nonunital) operator system. For a matrix ordered operator space $V$ with complete norm, we show that $V$ is completely isomorphic and complete order…
We introduce a novel framework consisting of a class of algebraic structures that generalize one-dimensional monoidal systems into higher dimensions by defining per-axis composition operators subject to non-commutativity and a global…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their…
Given an alternating trilinear form T on the V=F^n let L_T denote the set of T-singular lines in the projective space PV. These are all lines <a,b> for which the linear form T(a,b,.) is identically zero. Amongst the immense profusion of…
We study the class of noncommutative theories in $d$ dimensions whose spatial coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative theory,…
An adjoint pair is a pair of densely defined linear operators $A, B$ on a Hilbert space such that $\langle Ax,y\rangle=\langle x,By\rangle$ for $x\in \cD(A), y \in \cD(B).$ We consider adjoint pairs for which $0$ is a regular point for both…
We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation…
The study of a pair $(V_1,V_2)$ of commuting isometries is a classical theme. We shine new light on it by using the defect operator. In the cases when the defect operator is zero or positive or negative, or the difference of two mutually…
The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to a \textit{scalar product}, which we used to define \textit{orthogonals} in these…
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate…
A linear operator on a finite dimensional nonzero real vector space may not have an eigenvalue. We define a related notion of a true-pair of a linear operator, and then show that each linear operator on a finite dimensional nonzero real…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
Recall that an excedance of a permutation $\pi$ is any position $i$ such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting using toppling, we say that a permutation is toppleable if it…
We introduce a linear algebraic object called a bidiagonal pair. Roughly speaking, a bidiagonal pair is a pair of diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…
We reproduce the ${\cal N}=4$ supersymmetric mechanics on curved spaces, constructed earlier within the Hamiltonian formalism, using the superfield methods. We show that for any such mechanics, given by the metric and the third order…
Let $X$ be an Archimedean vector lattice. We investigate subalgebras of $\mathscr{L}(X)$ consisting of regular operators that contain all rank-one operators of the form $a \otimes \varphi_b$, where $a$ and $b$ are atoms of $X$ and…