Norms on self-adjoint symmetric tensor power of linear operators on Hilbert spaces (Yunied Puig de Dios, CMC)

We introduce a family of norms on the space of self-adjoint trace class symmetric tensor power of linear operators acting on an infinite-dimensional Hilbert space. Our technique is to extend to infinite dimension an original and nice idea of a very recent result by K. Aguilar,  Á. Chávez, S. R. Garcia and J. Volčič, in which the authors introduce a family of norms on the space of n x n  complex matrices induced by complete homogeneous symmetric polynomials. This is a work in progress paper, so it goes without saying that it will be very much appreciated any comment or/and suggestion coming from the audience. This is joint work with K. Aguilar, Á. Chávez and S. R. Garcia.