In recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th $xi$-symmetric tensor power of an operator and a matrix, when $xi$ is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power.
展开▼
机译：在最近的论文中，S。Carvalho和PJ Freitas获得了当运算符和矩阵为$ xi $时，所有阶，无穷和第m个 xi $对称张量的有向导数的公式。完全对称组的一个字符。还计算了这些导数的算子界范数。在本文中，为广义矩阵函数和每个对称张量幂建立了相似的结果。
展开▼
