Related papers: On cluster systems of tensor product systems of Hi…

Here we generalize the concept of spatial tensor product, introduced by Skeide, of two product systems via a pair of normalized units. This new notion is called amalgamated tensor product of product systems, and now the amalgamation can be…

We introduce the notion of additive units and roots of a unit in a spatial product system. The set of all roots of any unit forms a Hilbert space and its dimension is the same as the index of the product system. We show that a unit and all…

In this note we prove that the set of all uniformly continuous units on a product system over a C* algebra B can be endowed with the structure of left right B - B Hilbert module after identifying similar units by the suitable equivalence…

(See detailed abstract in the article.) We single out the correct class of spatial product systems (and the spatial endomorphism semigroups with which the product systems are associated) that allows the most far reaching analogy in their…

We introduce the notion of additive units, or `addits', of a pointed Arveson system, and demonstrate their usefulness through several applications. By a pointed Arveson system we mean a spatial Arveson system with a fixed normalised…

We prove that the spatial product of two spatial Arveson systems is independent of the choice of the reference units. This also answers the same question for the minimal dilation the Powers sum of two spatial CP-semigroups: It is…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…

Uncountably many mutually non-isomorphic product systems (that is, continuous tensor products of Hilbert spaces) of types II-0 and III are constructed by probabilistic means (random sets and off-white noises), answering four questions of W.…

We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference…

Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target…

We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global…

In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…

In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the…

Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for…

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…

In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…

It was proposed that the tensor product structure of the Hilbert space is uniquely determined by the Hamiltonian's spectrum, for most finite-dimensional cases satisfying certain conditions. I show that any such method would lead to…