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The noncommutative stable homotopy category $\mathtt{NSH}$ is a triangulated category that is the universal receptacle for triangulated homology theories on separable $C^*$-algebras. We show that the triangulated category $\mathtt{NSH}$ is…

We consider the tensorial Schur product $R \circ^\otimes S = [r_{ij} \otimes s_{ij}]$ for $R \in M_n(\mathcal{A}), S\in M_n(\mathcal{B}),$ with $\mathcal{A}, \mathcal{B}$ unital $C^*$-algebras, verify that such a `tensorial Schur product'…

We define a map which relates four dimensional classical stochastic matrices to qubit quantum channels. The map preserves the spectrum and the composition of processes. To do this we introduce the concept of Bloch tetrahedron which plays…

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of smooth sequence spaces $\lambda_0(A)$ of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which…

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…

Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category and we compute its…

We give conditions for when the tensor product of two positive maps between matrix algebras is a positive map. This happens when one map belongs to a symmetric mapping cone and the other to the dual cone. Necessary and sufficient conditions…

We explore the $k$-smoothness of bounded linear operators between Banach spaces, using the newly introduced notion of index of smoothness. The characterization of the $k$-smoothness of operators between Hilbert spaces follows as a direct…

We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a…

As proved in [16], for a Tychonoff space $X$, a locally convex space $C_{p}(X)$ is distinguished if and only if $X$ is a $\Delta$-space. If there exists a linear continuous surjective mapping $T:C_p(X) \to C_p(Y)$ and $C_p(X)$ is…

We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…

We first construct a real family of $SL(2,\mathbb{R})$-invariant symbol composition product $\{\sharp_\theta\}_{\theta\in,\mathbb{R}}$ on the analogue of the Schwartz space $S(\mathbb{D})$ on the hyperbolic plane…

The classical K\"{u}nneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove K\"{u}nneth-type theorems for the persistent homology of the categorical and tensor…

The program of matrix product states on tensor powers $\mathcal A^{\otimes \mathbb Z}$ of $C^\ast$-algebras, initiated in Comm. Math. Phys. {\bf 144}, 443-490 (1992), is re-assessed in a context where $\mathcal A$ is a generic nuclear…

The use of a tensor product perspective has enriched functional analysis and other important areas of mathematics and physics. The context of operator spaces is clearly no exception. The aim of this manuscript is to kick off the development…

A $k$-harmonic map is a critical point of the $k$-energy in the space of smooth maps between two Riemannian manifolds. In this paper, we prove that if $M^{n} (n\ge 3)$ is a CMC proper triharmonic hypersurface with at most three distinct…

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of power series spaces $\Lambda_0(\alpha)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\'echet space…

By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…

Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on complex Banach spaces $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\{1,\ldots,k\}$, and assume that at least…

We consider a closure operator $c$ of finite type on the space $SMod(\mathcal M)$ of thick $\mathcal K$-submodules of a triangulated category $\mathcal M$ that is a module over a tensor triangulated category $(\mathcal K,\otimes,1)$. Our…