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In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space M n ( X ) , when X is a numerical radius operator space. Moreover, we establish several inequalities for operator space numerical radius and the maximal numerical radius...
We consider bi-linear analogues of s -positivity for linear maps. The dual objects of these notions can be described in terms of Schmidt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite versions of Schmidt numbers cover various kinds of...
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps...
The additivity of the minimal output entropy and that of the χ -capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant...
We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex...
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