All Questions

Let $\Lambda_1,\dots,\Lambda_n$ be strictly positive definite operators in the Euclidean space $\mathbb{R}^d$. By an operator arithmetic-harmonic mean inequality with weights $\Lambda_i$ I mean the ...

Let $B\in M_3(\mathbb{C})$ and $S_3= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ \end{pmatrix} $. Suppose $I_3\otimes I_2+B\otimes X+B^*\otimes X^*\geq 0$ for all $2$...

Let $T\in\mathcal{B}(\mathcal{H})$ be a self-adjoint operator acting on a Hilbert space $\mathcal{H}$. Suppose $k\in\mathbb{N}$. Define $$\lambda_k(T)=\sup\limits_{\substack{\mathcal{M}\subseteq \...

Let $A(x), x\in (0,1)$ an $2\times n$ matrix, with $n\geq 2$. Consider the multiplication operator $K$ on $[L^2(0,1)]^n$ defined as $$K: f(x) \mapsto Kf(x)=A(x).f(x).$$ Intuitively, $$K: [L^2(0,1)]^n ...

Let $T\in\mathscr{B(\mathcal{H})}$ and $X\in M_n(\mathbb{C})$. Is the following statement true? If $W(B\otimes X)\subseteq W(B\otimes T)$ for any $B\in M_n$ then $W(B\otimes (X+I_n))\subseteq W(B\...

To immediately pose the question of interest to us, without first expanding upon its (quantum-information-theoretic) origin—we seek a univariate function $f$, for which we have the ("two-qubit ...