Related papers: Products and factorization in operator systems

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…

We provide a unified treatment of several commuting tensor products considered in the literature, including the tensor product of enriched categories and the Boardman-Vogt tensor product of operads and symmetric multicategories, subsuming…

A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous…

The Cuntz semigroup of a C*-algebra is an important invariant in the structure and classification theory of C*-algebras. It captures more information than K-theory but is often more delicate to handle. We systematically study the lattice…

Let $\A$ be a unital operator algebra and let $\alpha$ be an automorphism of $\A$ that extends to a *-automorphism of its $\ca$-envelope $\cenv (\A)$. In this paper we introduce the isometric semicrossed product $\A \times_{\alpha}^{\is}…

Let nbar=(n_1,...,n_r). The quotient space P_nbar:=(S^{n_1} x...x S^{n_r})/(x ~ -x)is what we call a projective product space. We determine the integral cohomology ring and the action of the Steenrod algebra. We give a splitting of Sigma…

Given a vector-space $~V~$ which is the tensor product of vector-spaces $A$ and $B$, we reconstruct $A$ and $B$ from the family of simple tensors $a{\otimes}b$ within $V$. In an application to quantum mechanics, one would be reconstructing…

In recent years finite tensor products of reproducing kernel Hilbert spaces (RKHSs) of Gaussian kernels on the one hand and of Hermite spaces on the other hand have been considered in tractability analysis of multivariate problems. In the…

The aim of this paper is two-fold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly, we discuss the existence of…

This work presents a rigorous characterization of inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators. We first deal with a general setting of continuous sesquilinear forms on a Hilbert space $\mathcal H$, and provide a…

We study the units in a tensor product of rings. For example, let k be an algebraically closed field. Let A and B be reduced rings containing k, having connected spectra. Let u \in A tensor_k B be a unit. Then u = a tensor_k b for some…

To a continuous action of a vector group on a $C^*$-algebra, twisted by the imaginary exponential of a symplectic form, one associates a Rieffel deformed algebra as well as a twisted crossed product. We show that the second one is…

We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…

In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of an appropriate…

The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…

The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids…

In this paper, we present a unified approach to problems of tensor product of quotient modules of Hilbert modules over $\mathbb{C}[z]$ and corresponding submodules of reproducing kernel Hilbert modules over $\mathbb{C}[z_1, \ldots, z_n]$…

We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection $P$ on a separable Hilbert space $\HH$, with the convergence in $L^2_\mathrm{loc}(\mathbb{R};\HH)$. It…

Let $K$ be a field. Let $f\in K[[x_{1},...,x_{r}]]$ and $g\in K[[y_{1},...,y_{s}]]$ be nonzero elements. If $X$ (resp. $Y$) is a matrix factorization of $f$ (resp. $g$), Yoshino had constructed a tensor product (of matrix factorizations)…

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…