Related papers: Kraus-Like Decompositions
This paper provides a complete characterization of quasicontractive groups and analytic $C_0$-semigroups on Hardy and Dirichlet space on the unit disc with a prescribed generator of the form $Af=Gf'$. In the analytic case we also give a…
Let $\g$ be a simple complex Lie algebra of type $G_2$, $F_4$, or $E_8$, and let $G$ be the unique connected simply connected Lie group with $\mathrm{Lie}(G)=\g$ with compact real form $K$. We prove a triangular decomposition theorem for…
Spaces of constant curvature and their motion groups are described most naturally in Cartesian basis. All these motion groups also known as CK groups are obtained from orthogonal group by contractions and analytical continuations. On the…
We prove some $K$-theoretic descent results for finite group actions on stable $\infty$-categories, including the $p$-group case of the Galois descent conjecture of Ausoni-Rognes. We also prove vanishing results in accordance with…
In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix…
The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…
In the framework of deformation quantization we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[\lambda]]-linear functionals obeying a formal variant of the usual KMS…
In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$…
We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $\Delta x=~(1-q)x$. Then, based on this, we develop the basic formalism of quantum…
We construct relativistic quantum Markov semigroups from covariant completely positive maps. We proceed by generalizing a step in Stinespring's dilation to a general system of imprimitivity and basing it on Poincar\'e group. The resulting…
In this paper, we study Vekua-type operators associated with diagonal operators on compact Lie groups. Characterizations of global hypoellipticity and global solvability properties are presented on classes of Vekua-type operators with…
Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…
An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional $C^*$-algebras) carry an action of a compact…
We investigate the structural and dynamical properties of a class of quantum channels on von Neumann algebras induced by averaging over operator groups via the Pettis integral. Utilizing the classical Yosida--Hewitt decomposition, we focus…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…
We show how to construct a compact quantum metric space from a proper continuous length function on an \'etale groupoid with compact unit space, where the unit space additionally has the structure of a compact metric space. Using compactly…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…
We introduce the notion of Krein-operator convexity in the setting of Krein spaces. We present an indefinite version of the Jensen operator inequality on Krein spaces by showing that if $(\mathscr{H},J)$ is a Krein space, $\mathcal{U}$ is…