Abstract
This paper is of expository nature. In the tensor product of two matrix spaces M m and M n we consider three natural cones; the first is the cone P 0 of positive semi-definite matrices, the second is the cone P + generated by tensor products of positive semi-definite matrices in the factor spaces, and the third cone P − is defined as the dual cone of P + . Correspondingly, in the tensor space identified with M mn , besides the spectral and the trace norms, we consider several tensor norms generated by sepectral and/or trace norms in the factor spaces. We will study relations among those norms as well as relations among the three kinds of order intervals in the tensor product.
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