# Questions tagged [tensor-products]

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### Tensor product of positive linear maps is positive

Let $\pi_1: A_1 \to B_1$ and $\pi_2: A_2 \to B_2$ be positive linear maps between complex $*$-algebras. Is the mapping $$\pi_1 \otimes \pi_2: A_1 \otimes A_2 \to B_1 \otimes B_2$$ again positive? I.e.,...
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### Is this "semi-tensor product" something recently invented? Are there other usages of it?

The context: I was reading a paper in which they used the following definition called "Semi-Tensor Product" (STP) or "Cheng" product (In honor to its "inventor" D. Cheng):...
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### Generalization of a standard algebraic group theory result for a tensor problem

$\DeclareMathOperator\GL{GL}$Let $X$, $Y$, $Z$ be $\mathbb{C}$-vector spaces, and let $A\subseteq X$ and $B\subseteq Y$ and $C\subseteq Z$ be linear subspaces. Let $V=X \otimes Y \otimes Z$, acted on ...
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### Spectral norm and "operator norm" for hypergraphs

Consider a $d$-regular, $k$-uniform hypergraph: the elements $S$ of its set $E$ of edges are subsets of $V$ of size $k$, and each vertex $v\in V$ is in $d$ edges. We can then define its adjacency ...
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### Basis of invariant tensors of rank n in three dimensions

[This is a question motivated by theoretical physics, so apologies if the language is rough...] In three dimensions the spaces of invariant (or isotropic) tensors of rank $n$ have dimensions 1, 0, 1, ...
### Inclusion $M(A) \otimes M(B)\subseteq M(A\otimes B)$ of multiplier algebras
Consider the following definitions given in Timmerman's book "An invitation to quantum groups and duality": m Further in the book, it is claimed that if $A$ and $B$ are non-degenerate ... 