Representations of Dirichlet Operator Algebras

半Dirichlet算子代数的交叉积与C*-覆盖

Crossed products and C*-covers of semi-Dirichlet operator algebras

该研究证明半Dirichlet算子代数的半DirichletC*-覆盖构成完备格且存在极大元，结合膨胀理论建立全交叉积与相对全交叉积的同构关系，最终得出半Dirichlet动力系统具有半Dirichlet全交叉积的结论。

Amenability and subexponential spectral growth rate of Dirichlet forms on von Neumann algebras

In this work we apply Noncommutative Potential Theory to prove (relative) amenability and the (relative) Haagerup Property $(H)$ of von Neumann algebras in terms of the spectral growth of Dirichlet forms. Examples deal with (inclusions of) countable discrete groups and free orthogonal compact quantum groups.

The Dirichlet Property for Tensor Algebras

We prove that the tensor algebra of a C*-correspondence $X$ is Dirichlet if and only if $X$ is a Hilbert bimodule. As a consequence, we point out and fix an error appearing in the proof of a famous result of Duncan. Secondly we answer a question raised by Davidson and Katsoulis concerning tensor algebras and semi-Dirichlet algebras, by giving an example of a Dirichlet algebra that cannot be described as the tensor algebra of any C*-correspondence. Furthermore we show that the adding tail technique, as extended by the author and Katsoulis, applies in a unique way to preserve the class of Hilber…

The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms

The Haagerup approximation property for a von Neumann algebra equipped with a faithful normal state $φ$ is shown to imply existence of unital, $φ$-preserving and KMS-symmetric approximating maps. This is used to obtain a characterisation of the Haagerup approximation property via quantum Markov semigroups (extending the tracial case result due to Jolissaint and Martin) and further via quantum Dirichlet forms.

Non Symmetric Dirichlet Forms on Semifinite von Neumann Algebras

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.

乘子品种和乘子代数的CNP狄利克雷级数核

Multiplier varieties and multiplier algebras of CNP Dirichlet series kernels

研究CNP狄利克雷级数核的乘子代数等距和代数同构问题，通过多项式方程确定乘子品种，从而分类其同构性，并解决McCarthy和Shalit提出的问题。