Research in the noncommutative dynamical systems through the method of functional analysis together with the research in the interplay between topological dynamical systems and operator theory

对应于拓扑动力系统的算子代数已被研究为C-闭积。另一方面，有Banach代数闭积。这些区别就是非自交闭理想的存在性。其中一个主要结果是：l^1的每个闭理想是自伴的当且仅当它的动力系统是自由的。代数的交换子是交换的极大Banach-代数，闭理想的交是非空的。证明了Banach-代数的存在性，并给出了极大交换子代数的存在投影。半亚正规算子是凸的吗？这是一个20年来的公开问题。关于这个问题，我们可以证明，如果对于单侧移位U，设S=T^2，则S是凸体。它发表在《线性和多线性代数》杂志上，标题为“关于半亚正规算子的数值范围的一点评论”。接下来，我们研究了Banach空间上的Polaroid算子。证明了如果Polaroid算子具有单值扩张性质，则Weyl定理对这类算子成立。证明了若算子T与Bishop性质和Polaroid拟相似，则T是Polaroid。这些结果发表在Journal of Mathematical Analysis and Applications上。

Operator algebras corresponding to topological dynamical systems have been studied as C-clossed products. On the other hand, there are Banach-algebra clossed products. These differences are the existence of non-self sdjoint closed ideal. One of the main results is the following : Every closed ideal of l^1 is self adjoint if and only if its dynamical system is free. Commutants of algebras are commutative maximal Banach-algebras and the intersection of closed ideals is non empty. We proved it for Banach-algebras and showed the existence projections to the maximal abelian subalgebras. As a more closing Are semi-hyponormal operators convexoid? This is a open problem for 20 years. About this problem, we could show that if, for the unilateral shift U, put S=T^2, then S is convexoid. It is published from the journal Linear and Multilinear Algebra with title"A remark on numerical range of semi-hyponormal operators". Next we studied Polaroid operators on a Banach space. We showed that if Polaroid operators have single value extension property, then Weyl's Theorem holds for these operators. Also we showed that if an operator T is quasi-similar with Bishop property and Polaroid, then T is Polaroid. These results are published from Journal of Mathematical Analysis and Applications.