Document Type: Original Article
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
In this paper, we define two new Schur and Kronecker-type products for block matrices. We present some equalities and inequalities involving traces of matrices generated by these products and in particular we give conditions under which the trace operator is sub-multiplicative for them. Also, versions in the block matrix framework of results of Das, Vashisht, Taskara and Gumus will be obtained.