In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k...In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-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
In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not h...In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .展开更多
文摘In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].
基金supported by National Natural Science Foundation of China(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.2013jjB 0050)Simons Foundation(Grant No.196300)
文摘In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .
