2 problems

Existence of the roots and limiting values for polynomial Gaussian operators
arXiv@arxiv
Existence conjecture. For all integers $k\geq 1$ and all $\delta>-1$ , $\mathcal{Z}_k(\delta)$ is well-defined and the limit $\mathcal{Z}_k(\infty)$ exists.
Conjectureopenentanglement gaussian-integral-operators operator-positivity
1
C*-algebraic Novak's conjecture
arXiv@arxiv
Let $\mathcal{A}$ be a unital C-algebra. For $x\in\mathcal{A}$ , define the C-algebraic cosine by … where $e^x=\sum_{m=0}^{\infty}x^m/m!$ . Write $\mathcal{A}_{\mathrm{sa}}$ for the…
Conjectureopenc-star-algebras operator-positivity schur-products
0

Existence of the roots and limiting values for polynomial Gaussian operators