相关论文: Non-Isomorphic Product Systems

We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…

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…

An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…

In these notes we prove two main results: 1) It is well-known that two strongly continuous $E_0$-semigroups on $B(H)$ can be paired if and only if they have anti-isomorphic Arveson systems. For a new notion of pairing (which coincides only…

Analytic continuation and functional equation of a Dirichlet series constructed from two (not necessarily cuspidal) holomorphic modular forms is discussed, where either weights of the modular forms or characters are not necessarily equal to…

We show that the product of any number of sequentially pseudocompact topological spaces is still sequentially pseudocompact. The definition of sequential pseudocompactness can be given in (at least) two ways: we show their equivalence. Some…

We associate two specific projective systems of probability spaces with any Tsirelson convolution system. If the projective limits of these systems exist, then we call the convolution system convergent and $K$-convergent, respectively. It…

Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…

We consider the concepts of continuous Bernoulli systems and non-commutative white noises. We address the question of isomorphism of continuous Bernoulli systems and show that for large classes of quantum L{\'e}vy processes one can make…

We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…

We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.

If $N \subset \R$ is a separable II$_1$-factor, the space $\Hom(N,\R)$ of unitary equivalence classes of unital *-homomorphisms $N \to \R$ is shown to have a surprisingly rich structure. If $N$ is not hyperfinite, $\Hom(N,\R)$ is an…

Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We…

In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values…

Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak…

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…