Related papers: Quotients, exactness, and nuclearity in the operat…
This paper explores the long journey from projective tensor products of a pair of Banach spaces, passing through the definition of nuclear operators still on the realm of projective tensor products, to the of notion of trace-class operators…
In this mostly expository note, we revisit the K\"unneth theorem in $K$-theory of nonnuclear C*-algebras. We show that, using examples considered by Skandalis, there are algebras satisfying the K\"unneth theorem for the minimal tensor…
We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minimal tensor products. Given two Fell…
We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
Nikol'skii known theorem for the kernels satisfying a condition $A^*_n$, is proved and for kernels from wider class. Explicit formulas for calculating the value of an approximation of classes $\W^{r, \beta}_{p, n} $ by convolution operators…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…
The $C^{\ast}$-algebra $\mathcal{U}_{nc}(n)$ is the universal $C^{\ast}$-algebra generated by $n^2$ generators $u_{ij}$ that make up a unitary matrix. We prove that Kirchberg's formulation of Connes' embedding problem has a positive answer…
We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by…
In analogy with the maximal tensor product of $C^*$-algebras, we define the ``maximal" tensor product $E_1\otimes_\mu E_2$ of two operator spaces $E_1$ and $E_2$ and we show that it can be identified completely isometrically with the sum of…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
In this paper we provide two characterizations of the maximal tensor product structure for the category of operator systems. The first one is via the schur tensor product; the second one employs the idea of the completely positive…
We demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…