Subsystems of Fock Need Not Be Fock: Spatial CP-Semigroups

Product systems and their representations: an approach using Fock spaces and Fell bundles

In this exposition we highlight product systems as the semigroup analogue of Fell bundles. Motivated by Fock creation operators we extend the definition of Fowler's product systems over unital discrete left-cancellative semigroups, via both a concrete and an abstract characterization. We next underline the importance of Fock spaces and Fell bundle methods for obtaining covariant representation results. First, the strongly covariant representations of Sehnem, for product systems over group embeddable semigroups, find their analogue here. Secondly, we give two solutions for the existence of the …

由半群相关的Fock表示产生的有界乘子代数

Bounded multiplier algebras arising from Fock representation associated to semigroups

本文引入与左消半群Fock表示相关的乘子代数，证明其为含单位Banach代数，群情形为C*-代数，并刻画了与Hardy代数及非交换Hardy代数的等距同构，最终利用算子空间技术证明其为算子代数。

The index of a subspatial product system over a Hilbert $C^*$-module -- an example

Recently, Bhat, Liebscher and Skeide exhibited an unusual example of product system of Hilbert $C^*$ modules. Namely, a subsystem of a Fock system, that is not Fock. Later, the authors defined the index of any product system of Hilbert $C^*$-modules, generalizing earlier partial definitions. In this note we compute the index of the mentioned interesting subsystem, and also we determine all its units.

Stopping the CCR flow and its isometric cocycles

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e., left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.

关于乘积系统的Fock协变性与离散作用下的约化Hao-Ng同构问题

On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions

本文刻画了乘积系统的等变Fock协变单射表示，证明其与Nica协变性和Toeplitz表示一致，并据此解决了离散群广义规范作用的约化Hao-Ng同构问题。

右LCM半群上乘积系统的余泛性与受控映射

Co-universality and controlled maps on product systems over right LCM-semigroups

该文研究右LCM半群上紧对齐乘积系统的C*-代数结构，结合受控映射、受控消去法与C*-包络理论，推导了余泛C*-代数刻画、核性与正合性条件及饱和受控映射下的系统性质等结果。