关于初等算子的本质谱与Taylor联合谱

本文将应用一些近来关于初等算子本质谱的最新成果,给出初等算子的本质谱关于Taylor联合谱及Taylor联合本质谱的表示。     

两组算子单调函数序列与严格Chaotic序

In this paper we introduce two sequences of operator functions and their dual functions:f_k(t)=((tlog t)~k-(t-1)~k)/(log~k 1t)(k=1,2,...),gk(t)=((t-1)~k-log~k t)/(log~k 1t)(k=1,2,...)and f_k~*=(t~klog~(k 1)t)/((tlog t)~k-(t-1)~k)(k=1,2,...),g_k~*(t)=(t~klog~(k 1)t)/((t-1)~k-log~k t)(k=1,2,...)definedon(0, ∞). We find that they are all operator monotone functions with respect to the strictly chaotic order and some ordinary orders among positive invertible operators.Indeed,we extend the results of the operator monotone function(tlog t -t 1)/(log~2t)which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].