Related papers: Complete positivity and self-adjointness
This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…
We investigate the spectrum of the generator induced on the space of Hilbert-Schmidt operators by a Gaussian quantum Markov semigroup with a faithful normal invariant state in the general case, without any symmetry or quantum detailed…
We introduce a preorder on an inverse semigroup $S$ associated to any normal inverse subsemigroup $N$, that lies between the natural partial order and Green's ${\mathscr J}$-relation. The corresponding equivalence relation $\simeq_N$ is not…
By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous QMSs. Moreover we prove that, when there exists a faithful normal invariant…
We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
We prove a Schoenberg-type correspondence for non-unital semigroups which generalizes an analogous result for unital semigroup proved by Michael Sch\"urmann. It characterizes the generators of semigroups of linear maps on $M_n(C)$ which are…
We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
We establish a Dynkin formula and a Courr\`ege-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator $A$ on $C_c^{\infty}(\mathbb{R}^d)$ satisfying the positive maximum principle can be…
We prove two results. (1) There is an absolute constant $D$ such that for any finite quasisimple group $S$, given 2D arbitrary automorphisms of $S$, every element of $S$ is equal to a product of $D$ `twisted commutators' defined by the…
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of…
In this article we prove that quasi-multiplicative (with respect to the usual length function) mappings on the permutation group $\SSn$ (or, more generally, on arbitrary amenable Coxeter groups), determined by self-adjoint contractions…
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give simple and complete characterizations of…
Embedding discrete Markov chains into continuous ones is a famous open problem in probability theory with many applications. Inspired by recent progress, we study the closely related questions of embeddability of real and positive operators…
We define a class of not necessarily linear $C_0$-semigroups $(P_t)_{t\geq0}$ on $C_b(E)$ (more generally, on $C_\kappa(E):=\frac1\kappa C_b(E)$, for some bounded function $\kappa$, which is the pointwise limit of a decreasing sequence of…
In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices…
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. We provide several characterizations of right amenable finitely generated subsemigroups of $z^2k[[z]]$ with the…
We give a proof of a result of D. Peterson's identifying the quantum cohomology ring of a Grassmannian with the reduced coordinate ring of a certain subvariety of $GL_n$. The totally positive part of this subvariety is then constructed and…