This paper is contributed to a fast algorithm for Hankel tensor–vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor–vector products by sketching the algorithm for both one-dimensional and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonal...

We introduce the injective tensor products and the projective tensor products of ordered vector spaces with Archimedean order unit and study their functorial properties. The local characterization of a nuclear space is given.

We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with $\sf{Ste}$ stereotype spaces. In particular, we give sufficient conditions under which identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle holds, where $\odot$ is injective product $\sf{Ste}$, $\...