MathOverflow

Let $\mathcal{B} = \{B_1,\ldots,B_m\}$, $\mathcal{C} = \{C_1,\ldots,C_m\}$, $\mathcal{D} = \{D_1,\ldots,D_m\}$ be three families of sets, with pairwise intersection between families not necessarily empty, and $A$ be another set such that $A \not\in ...

I am studying a family of non‑homogeneous linear complex differential equations and encountered the following limit. I would like an explicit counterexample, if one exists.
We consider $\eta \in L^\infty([1,+\infty), \mathbb{C})$ satisfying the following hypothesis $(H)$:...

Let $H$ be a separable Hilbert space, let $E\subset B(H)$ be a symmetrically normed operator ideal, and let $\tau$ be a continuous singular trace on an operator ideal containing $B(H)E$.
For $x\in E$, define
$$q_\tau(x) = \sup_{|B|_{B(H)}\le1}|\tau(B^*x)|$$...

There are numerical solutions to the above namely:
$(a,b,c,d)=(5,8,7,7)=(3,5,7,2)=(7,7,2,11)=(40,33,37,37)=(13,13,22,1)$
I took $(c=d)$ & got:$a=m^2-n^2,b=n^2-2mn,c=d=m^2-mn+n^2$