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...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].展开更多
文摘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].
